Development and application of Geobacillus stearothermophilus growth model for predicting spoilage of evaporated milk

Accepted Manuscript Development and application of Geobacillus stearothermophilus growth model for predicting spoilage of evaporated milk Myrsini Kakagianni, Maria Gougouli, Konstantinos P. Koutsoumanis PII:

S0740-0020(16)00002-2

DOI:

10.1016/j.fm.2016.01.001

Reference:

YFMIC 2512

To appear in:

Food Microbiology

Received Date: 8 June 2015 Revised Date:

7 December 2015

Accepted Date: 9 January 2016

Please cite this article as: Kakagianni, M., Gougouli, M., Koutsoumanis, K.P., Development and application of Geobacillus stearothermophilus growth model for predicting spoilage of evaporated milk, Food Microbiology (2016), doi: 10.1016/j.fm.2016.01.001. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Development and application of Geobacillus stearothermophilus growth model for

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predicting spoilage of evaporated milk

3 Myrsini Kakagianni, Maria Gougouli, Konstantinos P. Koutsoumanis*

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Laboratory of Food Microbiology and Hygiene, Department of Food Science and

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Technology, School of Agriculture, Faculty of Agriculture, Forestry and Natural

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Environment, Aristotle University of Thessaloniki, Thessaloniki, Greece 54124.

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*Corresponding author: Konstantinos P. Koutsoumanis, Aristotle University of Thessaloniki,

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Department of Food Science and Technology, School of Agriculture, Faculty of Agriculture,

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Forestry and Natural Environment, Thessaloniki, Greece 54124. Phone: +30 2310991647,

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Fax: +30 2310991647, e-mail: [email protected]

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Abstract

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The presence of Geobacillus stearothermophilus spores in evaporated milk constitutes an

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important quality problem for the milk industry. This study was undertaken to provide an

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approach in modeling the effect of temperature on G.stearothermophilus ATCC 7953 growth

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and in predicting spoilage of evaporated milk. The growth of G.stearothermophilus was

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monitored in tryptone soy broth at isothermal conditions (35-67°C). The data derived were

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used to model the effect of temperature on G. stearothermophilus growth with a cardinal type

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model. The cardinal values of the model for the maximum specific growth rate were

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Tmin=33.76°C,

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G.stearothermophilus was assessed in evaporated milk at Topt in order to adjust the model to

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milk. The efficiency of the model in predicting G.stearothermophilus growth at non-

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isothermal conditions was evaluated by comparing predictions with observed growth under

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dynamic conditions and the results showed a good performance of the model. The model was

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further used to predict the time-to-spoilage (tts) of evaporated milk. The spoilage of this

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product caused by acid coagulation when the pH approached a level around 5.2, eight

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generations after G.stearothermophilus reached the maximum population density (Nmax).

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Based on the above, the tts was predicted from the growth model as the sum of the time

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required for the microorganism to multiply from the initial to the maximum level (
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and

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Topt=61.82°C

µopt=2.068/h.

The

growth

of

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Tmax=68.14°C,

plus the time required after the
 to complete eight generations. The observed tts was

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very close to the predicted one indicating that the model is able to describe satisfactorily the

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growth of G.stearothermophilus and to provide realistic predictions for evaporated milk

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spoilage.

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Keywords: Geobacillus stearothermophilus, evaporated milk, growth kinetic model, time to

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spoilage, dynamic temperature, validation 2

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1.

Introduction The thermal processing of evaporated milk cannot guarantee the sterility of this product,

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since it is not able to eliminate some spores of bacteria, such as Geobacillus

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stearothermophilus, which are extremely heat resistant (Membré and van Zuijlen, 2011).

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Insufficient thermal treatment, high initial load of the spore-forming microorganism or

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spores, adhesive characteristics of spores that enhance their persistence in industrial plants or

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harsh conditions encountered in food ingredients processing and packaging technologies, as

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well as milk composition, are among the major factors explaining the emergence of

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thermophilic sporeformers, such as G. stearothermophilus, in thermally processed foods

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(André et al., 2013; Postollec et al., 2012; Simmonds et al., 2003; Yoo et al., 2006).

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Although a substantial effort in assessing inactivation kinetics of spores of G.

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stearothermophilus has been made (Ananta et al., 2001; Georget et al., 2014; Iciek et al.,

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2006; Watanabe et al., 2003), the presence of spores in the final product reflects a persistent

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quality problem for the canned food industry (André et al., 2013; Rigaux et al., 2013). As

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soon as the spores are exposed to conditions suitable for growth (nutrients, temperature), they

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germinate, outgrow and further grow, after an irreversible cascade of events. Τhe metabolic

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active cells then proceed to cell division up to a critical level, which may cause significant

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spoilage defects to thermally processed foods leading to significant economic losses for the

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dairy industry. Research results showed that the growth of this species in heat-treated milk

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and other products caused physicochemical changes like acidification (from saccharides)

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without gas production (Fields, 1970; Nazina et al., 2001), which in some cases led in

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coagulation (Burgess et al., 2010). Rigaux et al. (2014) reported that the time to spoilage of

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canned green beans corresponds to a population of 107 CFU/g, while Laudes et al. (2001)

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showed that colour change of a laboratory medium is observed when G. stearothermophilus

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reaches a level of 108 CFU/ml. However, limited information is available for the population

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concentration of the microorganism at which these changes occur in evaporated milk. One critical condition for the initiation of growth of G. stearothermophilus is the storage

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temperature. Research data support that germination, outgrowth and subsequent vegetative

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growth of G. stearothermophilus spores does not occur below 35-40°C (Burgess et al., 2010;

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Hill and Smythe, 2012; Llaudes et al., 2001; Ng and Schaffner, 1997; Oomes et al., 2007).

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However, the conditions prevailing in the supply chain of the evaporated milk are out of

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direct control of the manufacturer and often deviate from specifications. In particular, the

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storage of evaporated milk for long periods at improper and changing temperature conditions,

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like the ones existing in summer months in some countries, where the temperature is higher

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than 35°C, or in tropical and semitropical regions, may provoke the germination of spores, if

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these are present, the outgrowth and the subsequent growth of the vegetative cells of the

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organism.

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Obviously, G. stearothermophilus is a particular concern for the quality of evaporated

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milk and the estimation of the risk of spoilage constitutes a major target of the quality

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managers of the dairy industry, especially for the products that are going to be distributed in

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hot climate countries. For the development of a risk assessment of evaporated milk spoilage

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from G. stearothermophilus, a growth kinetic model is required that is able to predict the

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microbial behavior for both static and dynamic temperature conditions. However, within the

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domain of predictive microbiology, the supporting documentation for G. stearothermophilus

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growth kinetics is still very limited. Laudes et al. (2001) quantified the effect of inoculum

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size of G. stearothermophilus spores on spoilage time (change in colour) in a laboratory

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medium, while Ng and Schaffner (1997) developed a model for the effect of pH (5.5 to 7.0),

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temperature (45 to 60°C) and NaCl concentrations (0 to 1%) on growth of G.

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stearothermophilus in a laboratory medium (salty carrot medium). Later Ng et al. (2002)

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expanded the existing model (NaCl concentrations 0 to 1.5%) and validated it in tryptone soy

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broth and eight military ready-to-eat meals under constant temperature conditions.

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Nevertheless, information on the biokinetic range for growth considering the storage

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temperature and the impact of the food composition, which predominantly determine the

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behaviour of the organism, is still very limited (Mtimet et al., 2015).

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The objective of the present study was to develop a predictive model for the effect of

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temperature on growth of G. stearothermophilus and validate it in predicting spoilage of

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evaporated milk at dynamic temperature conditions simulating distribution and storage of the

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product. Such a product-specific model can be used for the development of a risk assessment

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approach for ensuring evaporated milk quality.

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2.

Materials and Methods

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2.1 Bacterial strain

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The type strain G. stearothermophilus ATCC 7953 was used for all experiments in the

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present study. The stock culture of the strain was stored frozen (-70°C) onto MicrobankTM

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porous beads (Pro-Lab Diagnostics, Ontario, Canada). The working culture was stored

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refrigerated (5°C) on nutrient agar (NA; Lab M Limited, Lancashire, United Kingdom) slants

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and was renewed bimonthly. The microorganism was activated by transferring a loopful from

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the NA slants into 10 ml nutrient broth (NB; Lab M Limited) and incubating at 55°C for 24h.

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The initial concentration of the inoculum was determined by surface plating on NA.

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2.2 Growth experiments in TSB

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The growth kinetic behaviour of the G. stearothermophilus was evaluated in tryptone soy

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broth (TSB; Lab M Limited) at temperatures of 35, 37.5, 40, 42.5, 45, 50, 52.5, 55, 57, 59,

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64, 65, 66 and 67°C. The above mentioned temperatures were selected in an attempt to cover

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the growth region of the species to the greatest possible extent, based on preliminary

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experiments. Maximum specific growth rate (µmax) values corresponding to each temperature were

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estimated by means of absorbance detection times of serially decimally diluted cultures using

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the automated turbidimetric system Bioscreen C (Oy Growth Curves Ab Ltd., Raisio,

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Finland) as described in the study of Lianou and Koutsoumanis (2011). The difference with

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the above study was that the 24-h culture of the microorganism was decimally diluted in TSB

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to a concentration of approximately 108 CFU/ml, while the range of initial concentrations

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obtained in the microtiter plates was approximately 106-102 CFU/well. For the temperatures

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from 37.5 to 59°C the microtiter plates were placed in the Bioscreen C, whilst for

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temperatures from 64 to 67°C, given the temperature limitations of the instrument, the

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microtiter plates were placed in high-precision incubators (model MIR 153, Sanyo Electric

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Co., Ora-Gun, Gunma, Japan), and the temperatures were monitored during incubation using

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electronic temperature-monitoring devices (Cox Tracer data logger; Cox Technologies,

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Belmont, NC, USA). Afterwards, optical density (OD) measurements were taken at 15-min

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and 20-min intervals for the temperatures from 37.5 to 59°C and from 64 to 67°C,

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respectively, using the wideband filter (420-580 nm) of the instrument, for a total time period

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such that a considerable OD change was observed, if possible, for all five decimally diluted

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cultures. The microtiter plates were agitated for 15 s at medium amplitude prior to the OD

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measurements. The detection times (h) of five serial decimal dilutions of the bacterial culture

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were plotted against the natural logarithm of their initial concentrations, and µmax values were

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determined by linear regression (Dalgaard and Koutsoumanis, 2001). One experiment was

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conducted for each temperature and five samples (e.g., quintuple wells of five serially diluted

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cultures) were analysed (n = 5).

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2.3 Growth experiments in evaporated milk For the experiments conducted in evaporated milk, G. stearothermophilus spores were

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used. The 24-h cultures in NB of the strain were heat shocked at 80°C for 10 min (Dogan et

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al., 2009), before inoculation into the product. The heat shock treatment was applied to G.

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stearothermophilus cultures in order to eliminate vegetative cells of Geobacillus endospores

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(Antolinos et al., 2012; Yuan et al., 2012). Then, the heat shocked cultures were centrifuged

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(6000rpm for 20min) in a refrigerated centrifuge (4°C) (model PK120R, ThermoElectron

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Corporation, Waltham, MA). The pellet was resuspended with 5 ml of quarter-strength

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Ringer’s solution (Lab M, Limited) and used for inoculation.

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The evaporated milk used for inoculation was a commercial evaporated milk

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(ingredients: skimmed milk, corn syrup, vegetable oils, milk fat, prebiotic fibers, soy lecithin,

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vitamins-C, PP, E, calcium pantothenate, A, B6, B1, D3, B2, folic acid, K1, D-biotin, B12-,

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minerals-potassium carbonate, ferrous sulphate, calcium citrate, zinc sulphate, copper

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sulphate, potassium iodide, sodium selenide). For this product, the initial aw and pH values

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were measured at 25°C using an Aqualab Series 3 water activity determination device

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(Decagon Devices Inc., Pullman, WA, United States) and a pH meter with a glass electrode

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(pH 211 Microprocessor, Hanna Instruments BV, Ijsselstein, the Netherlands), respectively.

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The pH (mean±st.dev.) and aw (mean±st.dev.) of evaporated milk were 6.16 (± 0.03) and

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0.994 (±0.03), respectively. Portions (200ml) of the evaporated milk were dispensed in 200ml

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Duran bottles and were inoculated with the appropriate dilution of the inoculum in order to

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obtain an initial concentration of ca. 103 CFU/ml. The artificially contaminated samples were

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then submerged in a preheated (62 ± 0.1°C) water bath (NB 9, 20, Nüve Sanayi Malzemeleri

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Imalat Ve Ticaret A.Ş., Ankara, Turkey), where the milk temperature reached 62°C. The

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above temperature was selected as optimum for growth based on the results derived from

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experiments conducted previously in TSB.

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For model validation, the behaviour of G. stearothermophilus spores in the evaporated

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milk was also studied under five different changing temperature scenarios designed in the

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laboratory simulating distribution and storage of the product in hot climate countries. For

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these experiments, high-precision programmable incubators (model MIR 153) were used. The

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fluctuating time–temperature protocols examined in this context were electronically recorded

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using cox tracer data loggers with the internal and external sensors monitoring temperature of

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the incubator and milk, respectively (with a time interval of 10 min).

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During incubation of the evaporated milk at 62°C or at dynamic temperature conditions,

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the inoculated samples were examined at appropriate time intervals in order i) to allow for an

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efficient kinetic analysis of microbial growth, ii) to monitor pH, and iii) to observe if there is

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any macroscopic change in the structure of milk (e.g., coagulation). Appropriate serial

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decimal dilutions of samples in Ringer’s solution were surface plated on NA plates for the

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enumeration of G. stearothermophilus population. Colonies were counted after incubation of

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plates at 55°C for 24 h. Four independent experiments were conducted with two replicates for

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the optimum temperature (n=8) and two independent experiments were conducted with two

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replicates for the non-isothermal scenarios (n=4).

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2.4 Data analysis

The effect of temperature on µmax, derived from the experiments conducted in TSB, was

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modelled using the Cardinal Model with Inflection (CMI) of Rosso et al. (1993):   =   ∙     =  

 

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!" [$  %$ %    & ' ]

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,

,

,

 ≤ 

(1)

 ≤  ≤  (2)  ≥ 

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where Tmin, Topt and Tmax are the theoretical minimum, optimum and maximum temperature

(°C) for growth, respectively, and *+,-./ is the optimum value for the maximum specific

growth rate (1/h) (when T=Topt). In order to stabilise the variance a square root transformation

of  was used.

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The values of Tmin, Topt and Tmax as well as the confidence and the predictions limits were

determined by fitting the estimated µmax values for the tested microorganism to the above

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model using the Excel v4 format of the curve-fitting program TableCurve 2D (Systat

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Software Inc., San Jose, CA, USA). The adequacy of the developed models to fit data was

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evaluated graphically and also by the coefficient of determination R2 and the Root Mean

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Square Error (RMSE) (Ratkowsky, 2004).

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The growth data (log CFU/ml) in the evaporated milk stored under isothermal

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temperature (62°C) were fitted to the primary model of Baranyi and Roberts (1994) using the

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program DMFit, in order to estimate the kinetic parameter for growth, maximum specific

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growth rate, µmax, in evaporated milk and the physiological state (ho) of the spores. The

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original dynamic model has an explicit solution for static situations (when the model

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parameters do not depend on time), which describes the natural logarithm of the cell

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concentration, y(t) = lnx(t), by the equation:

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0
= 01 +  3
− * 67 81 +

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@

: ; < / 5 : = >=?

(3)

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where µmax is the maximum specific growth rate of the cell population; ymax is the natural

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logarithm of the maximum population’s concentration; y0, the natural logarithm of the initial

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cell concentration; m is a curvature parameter characterizing the transition from the

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exponential to the stationary phase of growth and A(t) is a gradually delayed time variable

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described by the equation: 9

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3
=
+ A

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(4)

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our case are spores, to adjust to the new environment (Baranyi and Roberts, 1994).

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The prediction of growth under dynamic temperature was based on the assumption that

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after a temperature shift, the growth rate is adopted instantaneously to the new temperature

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environment. Equations (3) and (4) were used for the prediction of growth at dynamic

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(1) and (2). The “momentary” *+, was also used for the estimation of the number of

generations (G(T)) at dynamic temperature conditions using the following equation:

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temperature conditions based on the “momentary” *+, which was calculated from Equation

C A$G / %H/

E  = F1

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3.1

(5)

Results and Discussion

Growth experiments in TSB

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In the first part of this work the effect of temperature on G. stearothermophilus growth

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rate was investigated using the Bioscreen C method. All experiments were carried out with G.

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stearothermophilus cells in a laboratory medium (TSB) under isothermal storage conditions

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(35°C to 67°C). The average (±st.dev.) µmax increased from 0.293 (±0.016)/h at 37.5°C to

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1.449 (± 0.0004)/h at 64°C, while at temperatures >64°C a gradual decrease of µmax was

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observed. In the next step, the above experimental data (µmax) were modelled as a function of

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temperature using a CMI (Equation (1)), provided that this model incorporates parameters

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(Tmin, Topt, Tmax) which are regarded as biologically interpretable (Cuppers et al., 1997;

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Ratkowsky, 2004). The R2 and RMSE values (Table 1), as well as the graphical evaluation

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from the fitting curve (Fig. 1), indicated the satisfactory performance of the CMI in

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describing the effect of temperature on G. stearothermophilus µmax. The estimated values for

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the cardinal parameters Tmin, Tmax, Topt and the optimum maximum specific growth rate

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(  ) of G. stearothermophilus were found to be 33.76, 68.14, 61.82°C and 2.068 1/h,

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respectively (Table 1). It should be mentioned that the Tmin value constitutes the theoretical

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minimum temperature for growth, considering that at 35°C no growth was observed (data not

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shown). The above results are similar with those obtained in the study of Mtimet et al.

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(2015), in which it was found that the Tmin, Tmax and Topt (mean±st.dev.) were 38.52±3.22,

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68.02±5.62 and 57.59±1.75, respectively, although these data generated with a different

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strain of G. stearothermophilus with the surface plating technique.

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Interestingly, it was observed that G. stearothermophilus can grow adequately at

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temperatures which are sublethal or lethal for the majority of the microorganisms. There is

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strong evidence that the growth ability of thermophilic microorganisms, such as G.

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stearothermophilus, at high temperatures, is based on keeping their membrane fluidity

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constant (homeoviscous adaptation) (Sinenski, 1974). Particularly, the correct membrane

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function could be achieved due to the higher ratio of longer straight-chained saturated fatty

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acids in membrane lipids (Martins et al., 1990; Russell and Fukunaga, 1990; Suutari and

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Laakso, 1994; Zeikus, 1979). Except for the above theory, another factor, that could be

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responsible for the growth ability of thermophiles, is the production of sufficient amounts of

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thermostable gene products under elevated temperature conditions. Particularly, it has been

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observed a tendency of the purines levels to increase at the codon positions within the

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genome of thermophiles, compared to mesophiles, something which may correlate with

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mRNA thermostability (Cate et al., 1996, Wang and Hickey, 2002). Likewise, the trend that

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cytosine is preferred over thymine in many codons could play a crucial role in the greater

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thermostability, maybe due to the increased number of potential formed hydrogen bonds

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(Querol et al., 1996; Sadeghi et al., 2006; Singer and Hickey, 2003). In addition to that, at the

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protein level, the increased frequency of hydrophobic and/or charged amino acids (e.g.,

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glutamic acid, isoleucine, valine) and the simultaneously decreased frequency or removal of

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glutamine, which is a thermolabile amino acid, has been found that it has a great effect on

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thermostability of the encoded proteins probably because it reduces the possibility of the

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thermal unfolding process (Lynn et al., 2002, Singer and Hickey, 2003).

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3.2 Validation of the growth model for evaporated milk stored under dynamic temperature

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conditions

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By examining in quantitative terms the effect of temperature on G. stearothermophilus

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growth, a first picture of the biokinetic growth region of the microorganism is being provided

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(Fig. 1). However, in order to evaluate the performance of the developed model in predicting

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the growth behaviour of G. stearothermophilus spores in evaporated milk additional

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experiments were performed. More specifically, growth trials with the artificially

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contaminated evaporated milk with spores were conducted at a reference temperature of 62°C

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(Fig. 2), which was found to be the optimum temperature for the microorganism’s growth

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(Table 1). The obtained growth data were further expressed as a function of time, and via the

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use of the Baranyi and Roberts model (Equations (3) and (4)) the growth kinetic parameters

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were determined. The maximum specific growth rate (mean±st.dev.),  JK L°N , of G.

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stearothermophilus in the evaporated milk stored 62°C was 2.083±0.288 1/h, which was

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almost identical to that observed in TSB (2.068±0.036 1/h; Table 1), considering the standard

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deviation. Given the above similarity, for predictive modelling purposes the growth rate

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derived from TSB was selected for growth prediction at dynamic temperature conditions.

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At this point, it should be noted that the selected value of growth rate, used for the

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construction of the model (Equation (1)), may not be valid to other evaporated milk products 12

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with different composition than the examined one (Abee et al., 2011; Østergaard et al., 2014).

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As discussed in the literature, the presence and the concentrations of specific compounds in

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milk may exert different behavioural responses of the microorganism. Ljunger (1970) and

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Vinter (1969) reported that the existence of ions in milk, such as divalent cations (calcium,

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magnesium, potassium), can contribute to the outgrowth of mature spores and may be

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involved in the activation of sporulation. Moreover, there are several studies (Ashton and

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Busta, 1968; Cleverdon et al., 1949; Ståhl and Ljunger, 1976) supporting that the presence of

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divalent cations, such as calcium, magnesium and iron(II), and vitamins, like niacin and

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biotin, in milk have considerable effect on G. stearothermophilus growth and further on

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spoilage of evaporated milk. Arancia et al. (1980) reported that the presence of calcium

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cations stimulated Escherichia coli growth and reduced lag periods, while later the findings

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of Jurado et al. (1987) confirmed the above case for G. stearothermophilus demonstrating

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that magnesium cations above a critical concentration exert an inhibitory effect on

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microorganism’s growth. Given the above, it is obvious that in any case of use of the

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developed model, the appropriate corrections that correspond to specific products should be

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made.

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The developed model was further validated at dynamic temperature conditions.

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Prediction of growth at dynamic temperature conditions was based on the combination of the

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secondary model (Equation (1)) with the differential equations of the Baranyi and Roberts

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primary model (Equations (3) and (4)), which were numerically integrated with respect to

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time (Gougouli et al., 2008; Koutsoumanis, 2001; Xanthiakos et al., 2006). However, for

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predicting growth of G. stearothermophilus a selection of a ho value is required.

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In bacterial growth, ho represents the amount of “work” that a cell has to perform to

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adapt to its new environment. The “work” for adaptation is determined by the product of µmax

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and λ (lag phase) that is also called “physiological state” of the cells (Baranyi and Roberts,

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1994). Several studies have reported a relation between µmax and λ with their product µmax*λ

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being constant at different storage temperatures when the pre-inoculation history of the cells

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culture was the same (Baranyi and Roberts 1994, 1995; Gougouli et al., 2008; Koutsoumanis

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et al., 2006; Pin et al., 2002). In the experiments conducted in this study, the inoculum was

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constituted from spores which have been produced under a well defined environment. Based

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on the above, we assumed that the ho, which in this case refers to spore germination and

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outgrowth, is not affected by the storage temperature and we set its value to the one

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determined from the growth of G. stearothemophilus spores in evaporated milk under

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constant conditions 62°C, which was found to be 3.787. The Nmax was also set at 7.4 log

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CFU/ml based on the observation at 62°C.

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The predicted growth was compared to observed growth data derived from five

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experiments at changing temperatures (Figs. 3-7) simulating conditions of temperature abuses

328

during distribution and storage of the product in regions with hot climate and/or during warm

329

summer months (Weather Underground database, http://www.wunderground.com/). Abrupt

330

temperature upshifts and downshifts were included in the tested profiles in order to evaluate

331

model’s assumptions (i.e. growth rate is adopted instantaneously to the new temperature) at

332

extreme conditions representing a worst-case scenario for the performance of the model. In

333

general, at all temperature scenarios tested, the model adequately predicted the growth of G.

334

stearothermophilus in evaporated milk, suggesting that the assumptions made for growth

335

prediction were valid. Accurate predictions were obtained in the cases of temperature shifts

336

inside the growth region of the microorganisms (Figs. 3-5) as well as in scenarios including

337

temperatures lower from the Tmin (Figs. 6-7). For the last scenarios (Figs. 6-7) the results

338

showed that the bacterium adapts instantaneously to the new environment without presenting

339

any additional lag phase and grow with the expected µmax. Even after a storage period of

340

about 140 h at temperatures below Tmin, G. stearothermophilus was able to initiate growth

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341

when temperature increased to levels within the biokinetic range with a lag phase and a

342

growth rate very close to those predicted by the model (Fig. 6).

343

345

3.4. Prediction of the time-to-spoilage of the evaporated milk The

results

of

the

experiment

with

evaporated

RI PT

344

milk

inoculated

with

G.

stearothermophilus spores and stored at 62°C showed that spoilage of this product is due to

347

acid coagulation observed when the pH approaches a level around 5.2 (Fig. 2). This is in

348

agreement with previous studies (Hill and Smythe, 2012; Yoo et al., 2006) which have

349

demonstrated that G. stearothermophilus cells are producing acid, enhancing in this way the

350

formation of protein aggregates, something that is related with the unfolding and gelation of

351

β-lactoglobulin which has been found to be pH and temperature dependent. The decrease of

352

milk pH to the spoilage level was observed at a certain time (ts) after G. stearothermophilus

353

reached the maximum population density (Nmax = 107.4 CFU/ml). Considering that each

354

generation time (G) can be calculated under constant conditions as G=µmax/ln(2) the time ts

355

corresponded to an average of eight generations. Based on the above findings, the time-to-

356

spoilage (ttspred) was predicted from the growth model as following:

359 360

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OPQRS =


+ 8E 

EP

358



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357

SC

346

In Equation (6) the ttspred derives from the sum of the time (


(6)



) that is required for

361

the microorganism to multiply from the initial level to the maximum level (Nmax = 107.4

362

CFU/ml), which can be determined from the growth model, and the time that is required from

363

the cells after the


364

conditions. Generation Time (GT) under dynamic temperature conditions was estimated

365

from Equation (5).



to complete eight generations under the existing temperature

15

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The applicability of the model to predict spoilage of evaporated milk was evaluated by

367

comparing the predicted time to spoilage (ttspred) from Equation (6) with the time at which

368

coagulation was observed (ttsobs) for the five dynamic temperature experiments. A numerical

369

comparison between the ttsobs and ttspred is presented in Table 2. The ttsobs ranged from 29 to

370

223 h for the various temperature scenarios. As shown in Figs. 3-7, milk coagulation

371

coincided with a pH decrease to levels around 5.2 confirming the findings at static

372

temperature conditions (Fig. 2). For all the temperature scenarios examined the observed time

373

to spoilage was very close to the predicted one. The approach exploited in this research for

374

predicting the spoilage time of evaporated milk did not show any specific trend of

375

overestimation or underestimation considering the percent relative errors, which were ranging

376

from -8.7 to 4.5 (Table 2). The variation in the initial pH of evaporated milk was in general

377

limited. In particular, the initial pH (mean±st.dev.) of 4 milk batches tested at isothermal

378

conditions and 5 milk batches tested at dynamic temperature conditions was 6.16±0.03 and

379

6.08±0.13, respectively. The validation of the model indicated that the pH within the above

380

ranges did not significantly affect the performance of the model. However, application of the

381

model for milk with initial pH outside these ranges requires further validation studies.

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366

383

4.

EP

382 Conclusions

In conclusion, the model developed in the present study is able to describe satisfactorily

385

the effect of storage temperature on the growth of G. stearothermophilus in evaporated milk

386

and to provide realistic predictions for the rejection time of the product due to spoilage.

387

Beside the current value of this approach for the prediction of evaporated milk’s quality, the

388

developed model can be the basis for the construction of a quantitative microbial risk

389

assessment (QMRA) model for spoilage of evaporated milk from G.stearothermophilus.

390

However, as frequently commented by various researchers, the strain variability may have an

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important impact on the microbial risk assessment outcomes, and, for that reason it should be

392

assessed and taken into consideration for such approaches (Coleman et al., 2003; Delignette-

393

Muller and Rosso, 2000; Lianou and Koutsoumanis, 2013; Pouillot and Lubran, 2011). So

394

far, strain-depended differences in growth behaviour of G. stearothermophilus have not been

395

documented and the precision of a QMRA model would be inaccurate. Thus, for moving

396

from deterministic to stochastic modelling approaches further research on strain variability is

397

required. Furthermore, given that in practice, the spoilage defects of evaporated milks are

398

derived from low bacterial spore numbers, and the fact that the single spores are characterised

399

with heterogeneity in terms of lag time (Baranyi, 1998; Barker et al., 2005; Pin and Baranyi,

400

2006; Stringer et al., 2011), further studies on the effect of processing and storage conditions

401

on the variability of individual spores lag duration will increase the precision and credibility

402

of the model and allow a stochastic application for effective risk-based quality control of

403

evaporated milk.

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Acknowledgments

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This study was carried out with the financial support of “Understanding the impact of

407

manufacturing processes in the ecology of microorganisms that spoil-contaminate milk

408

products (ESL, evaporated milk) and fresh fruit juices – Development of molecular

409

methodologies and mathematical models for the prediction of their shelf-life” within the

410

framework of the action “Cooperation” (NSRF 2007-2013), that was co-financed by the

411

European Social Fund (ESF) and National Resources.

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References

413

Abee, T., Nierop Grout, M., Tempelaars, M., Zwietering, M., Moezelaar, R., van der Voort,

414

M., 2011. Review: Germination and outgrowth of spores of Bacillus cereus group

415

members: Diversity and role of germinant receptors. Food Microbiol. 28(2), 199-208.

416

Ananta, E., Heinz, V., Schlüter, O., Knorr, D., 2001. Kinetic studies on high-pressure

417

inactivation of Bacillus stearothermophilus spores suspended in food matrices. Innov.

418

Food Sci. Emerg. Technol. 2(4), 261-272.

SC

RI PT

412

André, S., Zuber, F., Remize, F., 2013. Thermophilic spore-forming bacteria isolated from

420

spoiled canned food and their heat resistance. Results of a French ten-year survey. Int. J.

421

Food Microbiol. 165(2), 134-143.

M AN U

419

Antolinos, V., Muñoz-Cuevas, M., Ros-Chumillas, M., Periago, P.M., Fernández, P.S., Le

423

Marc, Y., 2012. Modelling the effects of temperature and osmotic shifts on the growth

424

kinetics of Bacillus weihenstephanensis in broth and food products. Int. J. Food

425

Microbiol. 158(1), 36-41.

TE D

422

Arancia, G., Belli, S., Donelli, G., Trovalusci, P., 1980. Ultrastructural changes in

427

Escherichia coli grown in divalent cation-deficient medium. J. Gen. Microbiol. 119(1),

428

155-164.

430 431 432 433 434 435 436

Ashton, D.H., Busta, F.F., 1968. Milk components inhibitory to Bacillus stearothermophilus. J. Dairy Sci. 51(6), 842-847.

AC C

429

EP

426

Baranyi, J., 1998. Comparison of stochastic and deterministic concepts of bacterial lag. J. Theor. Biol. 192(3), 403-408.

Baranyi, J., Roberts, T.A., 1994. Review: A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23(3-4), 277-294. Baranyi, J., Roberts, T.A., 1995. Mathematics of predictive food microbiology. Int. J. Food Microbiol. 26(2), 199-218.

18

ACCEPTED MANUSCRIPT

437

Barker, G.C., Malakar, P.K., Peck, M.W., 2005. Germination and growth from spores:

438

variability and uncertainty in the assessment of food borne hazards. Int. J. Food

439

Microbiol. 100(1-3), 67-76.

441

Burgess, S.A., Lindsay, D., Flint, S.H., 2010. Review: Thermophilic bacilli and their

RI PT

440

importance in dairy processing. Int. J. Food Microbiol. 144(2), 215-225.

Cate, J.H., Gooding, A.R., Podell, E., Zhou, K., Golden, B.L., Szewczak, A.A., Kundrot,

443

C.E., Cech, T.R., Doudna, J.A., 1996. RNA tertiary structure mediation by adenosine

444

platforms. Science 273(5282), 1696-1699.

446

Cleverdon, R.C., Pelczar, M.J.,Jr., Doetsch, R.N., 1949. The vitamin requirements of

M AN U

445

SC

442

stenothermophilic aerobic sporogenous bacilli. J. Bacteriol. 58(4), 523-526.

447

Coleman, M.E., Tamplin, M.L., Phillips, J.G., Marmer, B.S., 2003. Influence of agitation,

448

inoculums density, pH, and strain on the growth parameters of Escherichia coli

449

O157:H7-relevance to risk assessment. Int. J. Food Microbiol. 83, 147–160. Cuppers, H.G.A.M., Oomes, S., Brul, S., 1997. A model for the combined effects of

451

temperature and salt concentration on growth rate of food spoilage molds. Appl. Environ.

452

Microbiol. 63(10), 3764-3769.

TE D

450

Dalgaard, P., Koutsoumanis, K., 2001. Comparison of maximum specific growth rates and

454

lag times estimated from absorbance and viable count data by different mathematical

455

models. J. Microbiol. Methods 43(3), 183-196.

457

AC C

456

EP

453

Delignette-Muller, M.L., Rosso, L., 2000. Biological variability and exposure assessment. Int. J. Food Microbiol. 58, 203–212.

458

Dogan, Z., Weidendorfer, K., Müller-Merbach, M., Lembke, F., Hinrichs, J., 2009.

459

Inactivation kinetics of Bacillus spores in batch- and continuous-heating systems. LWT -

460

Food Sci. Technol. 42(1), 81-86.

461

Fields, M.L., 1970. The flat sour bacteria. Adv. Food Res. 18, 163-217.

19

ACCEPTED MANUSCRIPT

462

Georget, E., Miller, B, Aganovic, K., Callanan, M., Heinz, V., Mathys, A., 2014. Bacterial

463

spore inactivation by ultra-high pressure homogenization. Innov. Food Sci. Emerg.

464

Technol. 26, 116-123. Gougouli, M., Angelidis, A.S., Koutsoumanis, K., 2008. A study on the kinetic behavior of

466

Listeria monocytogenes in ice cream stored under static and dynamic chilling and

467

freezing conditions. J. Dairy Sci. 91(2), 523-530.

RI PT

465

Hill, B.M., Smythe, B.W., 2012. Endospores of thermophilic bacteria in ingredient milk

469

powders and their significance to the manufacture of sterilized milk products: an

470

industrial perspective. Food Rev. Int. 28(3), 299-312.

472

M AN U

471

SC

468

Iciek, J., Papiewska, A., Molska, M., 2006. Inactivation of Bacillus stearothermophilus spores during thermal processing. J. Food Eng. 77(3), 406-410.

Jurado, A.S., Santana, A.C., Da Costa, M.S., Madeira, V.M.C., 1987. Influence of divalent

474

cations on the growth and morphology of Bacillus stearothermophilus. J.Gen. Microbiol.

475

133(3), 507-513.

476 477

TE D

473

Koutsoumanis K. (2001). Predictive modeling of the shelf life of fish under nonisothermal conditions. Appl. Environ. Microbiol. 67(4), 1821-1829. Koutsoumanis, K., Stamatiou, A., Skandamis, P., Nychas, G.-J.E., 2006. Development of a

479

microbial model for the combined effect of temperature and pH on spoilage of ground

480

meat, and validation of the model under dynamic temperature conditions. Appl. Environ.

AC C

481

EP

478

Microbiol. 72(1), 124-134.

482

Laudes, M.K., Zhao, L., Duffy, S., Schaffner, D.W., 2001. Simulation and modelling of the

483

effect of small inoculums size on time to spoilage by Bacillus stearothermophilus. Food

484

Microbiol. 18(4), 395-405.

485

Lianou, A., Koutsoumanis, K.P., 2011. Effect of the growth environment on the strain

486

variability of Salmonella enterica kinetic behaviour. Food Microbiol. 28(4), 828-837.

20

ACCEPTED MANUSCRIPT

488 489 490 491 492

Lianou, A., Koutsoumanis, K.P., 2013. Strain variability of the behavior of foodborne bacterial pathogens: A review. Int. J. Food Microbiol. 167, 310-321. Ljunger, C., 1970. On the nature of the heat resistance of thermophilic bacteria. Physiol. Plant. 23(2), 351-364.

RI PT

487

Lynn, D.J., Singer, G.A.C., Hickey, D.A., 2002. Synonymous codon usage is subject to selection in thermophilic bacteria. Nucleic Acids Res. 30(19), 4272-4277.

Martins, L., Jurado, A.S., Madeira, V.M.C., 1990. Composition of polar lipid acyl chains of

494

Bacillus stearothermophilus as affected by temperature and calcium. Biochim. Biophys.

495

Acta 1045(1), 17-20.

M AN U

SC

493

496

Membré J.-M., van Zuijlen A., 2011. A probabilistic approach to determine thermal process

497

setting parameters: application for commercial sterility of products. Int. J. Food

498

Microbiol. 144(3), 413-420.

Mtimet, N., Trunet, C., Mathot, A.-G., Venaille, L., Leguérinel, I., Coroller, L., Couvert, O.,

500

2015. Modeling the behavior of Geobacillus stearothermophilus ATCC 12980

501

throughout its life cycle as vegetative cells or spores using growth boundaries. Food

502

Microbiol. 48, 153-162.

TE D

499

Nazina, T.N., Tourova, T.P., Poltaraus, A.B., Novikova, E.V., Grigoryan, A.A., Ivanova,

504

A.E., Lysenko, A.M., Petrunyaka, V.V., Osipov, G.A., Belyaev, S.S., Ivanov, M.V.,

505

2001. Taxonomic study of aerobic thermophilic bacilli: descriptions of Geobacillus

507 508

AC C

506

EP

503

subterraneus gen. nov., sp. nov. and Geobacillus uzenensis sp. nov. from petroleum reservoirs and transfer of Bacillus stearothermophilus, Bacillus thermocatenulatus, Bacillus thermoleovorans, Bacillus kaustophilus, Bacillus thermoglucosidasius and

509

Bacillus

thermodenitrificans

to

Geobacillus

as

the

new

combinations

G.

510

stearothermophilus, G. thermocatenulatus, G. thermoleovorans, G. kaustophilus, G.

21

ACCEPTED MANUSCRIPT

511

thermoglucosidasius and G. thermodenitrificans. Int. J. Syst. Evol. Microbiol. 51(2),

512

433-446. Ng, T.M., Schaffner, D.W., 1997. Mathematical models for the effects of pH, temperature,

514

and sodium chloride on the growth of Bacillus stearothermophilus in salty carrots. Appl.

515

Environ. Microbiol. 63(4), 1237-1243.

RI PT

513

Ng, T.M., Viard, E., Caipo, M.L., Duffy, S., Schaffner, D.W., 2002. Expansion and

517

validation of a predictive model for the growth of Bacillus stearothermophilus in military

518

rations. J. Food Sci. 67(5), 1872-1878.

SC

516

Oomes, S.J.C.M., van Zuijlen, A.C.M., Hehenkamp, J.O., Witsenboer, H., van der Vossen,

520

J.M.B.M., Brul, S., 2007. The characterization of Bacillus spores occurring in the

521

manufacturing of (low acid) canned products. Int. J. Food Microbiol. 120(1-2), 85-94.

522

Østergaard, N.B., Eklöw, A., Dalgaard, P., 2014. Modelling the effect of lactic acid bacteria

523

from starter- and aroma culture on growth of Listeria monocytogenes in cottage cheese.

524

Int. J. Food Microbiol. 188, 15-25.

526

TE D

525

M AN U

519

Pin, C., Baranyi, J., 2006. Kinetics of single cells: observation and modelling of a stochastic process. Appl. Environ. Microbiol. 72(3), 2163-2169. Pin, C., García de Fernando, G.D., Ordóñez, J.A., Baranyi, J., 2002. Analysing the lag-

528

growth rate relationship of Yersinia enterocolitica. Int. J. Food Microbiol. 73(2-3), 197-

529

201.

AC C

EP

527

530

Postollec, F., Mathot, A.-G., Bernard, M., Divanac'h, M.-L., Pavan, S., Sohier, D., 2012.

531

Tracking spore-forming bacteria in food: From natural biodiversity to selection by

532

processes. Int. J. Food Microbiol. 158(1), 1-8.

533

Pouillot, R., Lubran, M.B., 2011. Predictive microbiology models vs. modeling microbial

534

growth within Listeria monocytogenes risk assessment: what parameters matter and why.

535

Food Microbiol. 28, 720–726.

22

ACCEPTED MANUSCRIPT

537 538 539

Querol, E., Perez-Pons, J.A., Mozo-Villarias, A., 1996. Analysis of protein conformational characteristics related to thermostability. Protein Eng. 9(3), 265-271. Ratkowsky, D.A., 2004. Model fitting and uncertainty, in: McKellar, R.C., Lu, X. (Eds.), Modelling Microbial Responses in Food, CRC Press, Boca Raton, Florida, pp. 151-196.

RI PT

536

Rigaux, C., Ancelet, S., Carlin, F. Nguyen-thé, C., Albert, I. (2013). Inferring an augmented

541

bayesian network to confront a complex quantitative microbial risk assessment model

542

with durability studies: Application to Bacillus cereus on a courgette purée production

543

chain. Risk Anal. 33(5), 877-892.

SC

540

Rigaux, C., André, S., Albert, I., Carlin, F., 2014. Quantitative assessment of the risk of

545

microbial spoilage in foods. Prediction of non-stability at 55 °C caused by Geobacillus

546

stearothermophilus in canned green beans. Int. J.Food Microbiol. 171, 119-128.

M AN U

544

Rosso, L., Lobry, J.R., Flandrois, J.P., 1993. An unexpected correlation between cardinal

548

temperatures of microbial growth highlighted by a new model. J. Theor. Biol. 162(4),

549

447-463.

552 553 554 555 556

psychrophilic and thermophilic bacteria. FEMS Microbiol. Rev. 75(2-3), 171-182. Sadeghi, M., Naderi-Manesh, H., Zarrabi, M., Ranjbar, B., 2006. Effective factors in

EP

551

Russel, N.J., Fukunaga, N., 1990. A comparison of thermal adaptation of membrane lipids in

thermostability of thermophilic proteins. Biophys. Chem. 119(3), 256-270. Simmonds, P., Mossel, B.L., Intaraphan, T., Deeth, H.C., 2003. Heat resistance of Bacillus

AC C

550

TE D

547

spores when adhered to stainless steel and its relationship to spore hydrophobicity. J. Food Prot. 66(11), 2070-2075.

557

Sinensky, M. (1974). Homeoviscous adaptation-a homeostatic process that regulates the

558

viscosity of membrane lipids in Escherichia coli (spin-labeling/phase transitions). Proc.

559

Natl. Acad. Sci. 71(2), 522-525.

23

ACCEPTED MANUSCRIPT

563 564 565 566 567 568 569

Ståhl, S., Ljunger, C., 1976. Calcium uptake by Bacillus stearothermophilus: a requirement for thermophilic growth. FEBS Lett. 63(1), 184-187.

RI PT

562

codon usage, amino acid composition and nucleotide content. Gene 317, 39-47.

Stringer, S.C., Webb, M.D., Peck, M.W., 2011. Review: Lag time variability in individual spores of Clostridium botulinum. Food Microbiol. 28(2), 228-235.

Suutari, M., Laakso, S., 1994. Microbial fatty acids and thermal adaptation. Crit. Rev.

SC

561

Singer, G.A.C., Hickey, D.A., 2003. Thermophilic prokaryotes have characteristic patterns of

Microbiol. 20(4), 285-328.

Vinter, V., 1969. Physiology and biochemistry of sporulation, in: Gould, G.W., Hurst, A.

M AN U

560

(Eds.), The Bacterial Spore. Academic Press, London, UK, pp. 73-124.

570

Wang, H.-c., Hickey, D.A., 2002. Evidence for strong selective constraint acting on the

571

nucleotide composition of 16S ribosomal RNA genes. Nucleic Acids Res. 30(11), 2501-

572

2507.

Watanabe, T., Furukawa, S., Hirata, J., Koyama, T., Ogihara, H., Yamasaki, M., 2003.

574

Inactivation of Geobacillus stearothermophilus spores by high-pressure carbon dioxide

575

treatment. Appl. Environ. Microbiol. 69(12), 7124-7129.

TE D

573

Xanthiakos, K., Simos, D., Angelidis, A.S., Nychas, G.J.-E., Koutsoumanis, K., 2006.

577

Dynamic modeling of Listeria monocytogenes growth in pasteurized milk. J. Appl.

578

Microbiol. 100(6), 1289-1298.

580

AC C

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EP

576

Yoo, J.-A., Hardin, M.T., Chen, X.D., 2006. The influence of milk composition on the growth of Bacillus stearothermophilus. J. Food Eng. 77(1), 96-102.

581

Yuan, D.-D., Liu, G.-C., Ren, D.-Y., Zhang, D., Zhao, L., Kan, C.-P., Yang, Y.-Z., Ma, W.,

582

Li, Y., Zhang, L.-B., 2012. A survey on occurrence of thermophilic bacilli in

583

commercial milk powders in China. Food Control 25(2), 752-757.

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Microb. Technol. 1(4), 243-252.

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Zeikus, J.G., 1979. Thermophilic bacteria: ecology, physiology and technology. Enzyme

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Tables

587

Table 1. Estimated values and statistics for the parameters of the Cardinal Model with

588

Inflection (Equation (1)) describing the effect of temperature on the maximum specific

589

growth rate (µmax) of Geobacillus stearothermophilus ATCC 7953 in tryptone soy broth. Lower 95% CLb

2.068±0.036

1.996

2.140

Tmax

68.14±0.15

67.83

68.44

Tmin

33.76±0.36

33.03

Topt

61.82±0.20

61.43

a

±: Standard Error

b

CL: Confidence Limits

592

c

RMSE: Root Mean Square Error

593

d

R2: Coefficient of determination

0.977

34.48 62.21

AC C

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591

0.0033

R2d

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*+,-./ (1/h)

Upper 95% CLb RMSEc

SC

Estimated Valuea

Parameter

590

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586

26

ACCEPTED MANUSCRIPT

594

Table 2. Comparison between observed and predicted spoilage time of the evaporated milk,

595

stored under nonisothermal conditions, by Geobacillus stearothermophilus ATCC 7953.

a

597

b

598

c

599

d

UUVZ[\] c (h)

%REd

1 (Fig. 3)

35.0

36.75

-4.8

2 (Fig. 4)

29.0

28.0

3.6

3 (Fig. 5)

88.0

91.5

-3.8

4 (Fig. 6)

223.0

244.33

-8.7

5 (Fig.7)

78.0

74.67

4.5

RI PT

UUVWXY b (h)

SC

596

Temperature profile (figure)a



O^_` , observed spoilage time

M AN U

Each figure corresponds to the indicated temperature profile

OPQRS , predicted spoilage time based on the Equation (6). RE: Relative Error =

CCa-bc  CCa.deH CCa.deH

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600

× 100

27

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Figure Captions

602

Fig. 1. Effect of temperature on the maximum specific growth rate (µmax) of Geobacillus

603

stearothermophilus ATCC 7953 in tryptone soy broth, fitted in the Cardinal Model with

604

Inflection (solid line) (Equation (1)). Points (○) represent observed values of the µmax. The

605

dotted and the discontinuous lines depict the 95% confidence and the prediction limits,

606

respectively, of the effect of temperature on the maximum specific growth rate.

607

Fig. 2. Growth kinetics of Geobacillus stearothermophilus ATCC 7953 vegetative cells

608

derived from spores (●) in evaporated milk and pH changes (○) during storage at optimum

609

growth temperature (62°C). The black solid line (▬) depicts the fitting of the Baranyi and

610

Roberts model (Equation (3)) to the growth data. The white point (∆) is showing the observed

611

time of evaporated milk coagulation. Each point is a mean of eight values. Vertical and

612

horizontal bars indicate the standard deviation.

613

Fig. 3. Comparison between observed (points) and predicted (lines) growth of Geobacillus

614

stearothermophilus ATCC 7953 in the evaporated milk stored under periodically changing

615

temperature condition 1. Discontinuous lines indicate milk pH (- - -) and temperature

616

changes (------).

617

Fig. 4. Comparison between observed (points) and predicted (lines) growth of Geobacillus

618

stearothermophilus ATCC 7953 in evaporated milk stored under periodically changing

619

temperature condition 2. Discontinuous lines indicate milk pH (- - -) and temperature

620

changes (------).

621

Fig. 5. Comparison between observed (points) and predicted (lines) growth of Geobacillus

622

stearothermophilus ATCC 7953 in the evaporated milk stored under periodically changing

623

temperature (24h at 37°C, 12h at 42°C and 24h at 45°C). Discontinuous lines indicate milk

624

pH (- - -) and temperature changes (------).

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Fig. 6. Comparison between observed (points) and predicted (lines) growth of Geobacillus

626

stearothermophilus ATCC 7953 in the evaporated milk stored under periodically changing

627

temperature (78h at 20°C, 59h at 25°C and 163h at 40°C). Discontinuous lines indicate milk

628

pH (- - -) and temperature changes (------).

629

Fig. 7. Comparison between observed (points) and predicted (solid line) growth of

630

Geobacillus stearothermophilus ATCC 7953 in the evaporated milk stored under periodically

631

changing temperature (6h at 50°C, 12h at 30°C and 24h at 42°C). Discontinuous lines

632

indicate milk pH (- - -) and temperature changes (------).

AC C

EP

TE D

M AN U

SC

RI PT

625

29

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1 2

2.5

3 2.0

6 7 8 9

RI PT

µmax (1/h)

5 1.5

1.0

0.5

10 11

0.0 40

60

Temperature (°C)

13

EP

TE D

Fig. 1.

AC C

14

50

M AN U

30

12

SC

4

70

80

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1

SC

RI PT

2 3 4 5 6 7 8 9 10 11 12 13 14

EP

TE D

Fig. 2.

AC C

16

M AN U

15

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60 7.0

7,0

8

6.5 50

6,5

6

6.0

40

4

5.5

30 5.0

13

0 0

14

10

Time (h)

EP

TE D

Fig. 3.

AC C

16 17

30

40

M AN U

15

20

SC

2

12

6,0

50

20 4.5

5,5

5,0

4,5

pH

pH temperature

RI PT

Log10 CFU/ml

10

Temperature (°C)

1 2 3 4 5 6 7 8 9 10 11

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1

Log10 CFU/ml

5 6 7

40

5,5

4

30 5,0

0

11

10

Time (h)

12

EP

TE D

Fig. 4.

AC C

13

20

30

M AN U

0

SC

2

10

6,5

6,0

6

8 9

6,5 50

RI PT

8

4

7,0

40

4,5 20

6,0

5,5

5,0

4,5

pH

pH temperature

3

7,0 60

Temperature (°C)

10

2

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1 7,0

8

45 6.5

6,5

6

40 6.0

6 7 8

4

35 5.5

2

30 5.0

9 10

0 0

11

20

40

60

80

100

M AN U

Time (h)

12 13

6,0

Fig. 5.

AC C

EP

TE D

14

25 4.5 120

5,5

5,0

4,5

pH

5

RI PT

Log10 CFU/ml

4

SC

3

pH temperature

Temperature (°C)

50 7.0

10

2

ACCEPTED MANUSCRIPT

1 7,0

8

40 6.5

6,5

6

35 6.0

RI PT 30

4

5.5 25

0 50

100

150

200

250

M AN U

0

Time (h)

AC C

EP

TE D

Fig. 6.

5,5

5.0 20

5,0

15 4.5 300

4,5

SC

2

6,0

pH

pH temperature

Temperature (°C)

45 7.0

10

Log10 CFU/ml

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

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60 7.0

7.0

8

6.5 50

6.5

6

6.0

40

4

5.5

30 5.0

0 0

10

20

30

40

60

70

M AN U

Time (h)

50

SC

2

AC C

EP

TE D

Fig. 7.

80

20 4.5

5.5

5.0

4.5

pH

6.0

RI PT

pH temperature

Temperature (°C)

10

Log10 CFU/ml

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

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2

Highlights •

3 4

Geobacillus stearothermophilus constitutes one of the most important quality problem for evaporated milk.

•

5

A cardinal type model was used to model the effect of the temperature on microbial

RI PT

1

growth. •

The model adequately predicted the growth in milk under dynamic conditions.

7

•

The developed model was used to predict the time-to-spoilage of evaporated milk.

8

•

The proposed growth model can be applied for the development of a risk assessment approach for assuring evaporated milk quality.

M AN U

9

SC

6

AC C

EP

TE D

10