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Chapter 40 : Predictive Microbiology

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Abstract:

Predictive microbiology focuses on the quantitative description and prediction of the behavior (growth, survival, and inactivation) of pathogenic and spoilage microorganisms in food products. A first section of this chapter focuses on modeling trends up to now. The classical primary and secondary model approach, used to describe growth and inactivation, as well as probabilistic models used to describe the growth/no growth (G/NG) boundary, are discussed. In the following section, contemporary and future modeling trends are listed and the extension of existing models is discussed, including (i) the trend for the incorporation of multiple environmental factors and (ii) the incorporation of the specific aspect of food structure. To move from the macroscopic to the meso- and microscopic levels, the concepts of metabolic networks and individual-based models (IbM) have been introduced. The chapter provides a short overview of mesoscopic models, i.e., models that describe the dynamics of the population as a combination of different compartments. The last section deals with the transfer of predictive microbiology as a tool for food safety and food quality from academia to industry. Specifically, a series of software tools is listed. In this context, lactic acid bacteria are increasingly being investigated, not only because of their ability to inhibit outgrowth of pathogens and spoilage microorganisms in fermented foods but also for their potential to act as protective cultures in minimally processed foods.

Citation: Van Derlinden E, Mertens L, Van Impe J. 2013. Predictive Microbiology, p 997-1022. In Doyle M, Buchanan R (ed), Food Microbiology. ASM Press, Washington, DC. doi: 10.1128/9781555818463.ch40
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Schematic representation of the stoichiometric modeling framework ( ). doi:10.1128/9781555818463.ch40f1

Citation: Van Derlinden E, Mertens L, Van Impe J. 2013. Predictive Microbiology, p 997-1022. In Doyle M, Buchanan R (ed), Food Microbiology. ASM Press, Washington, DC. doi: 10.1128/9781555818463.ch40
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1. Abou-Zeid, K. A.,, T. P. Oscar,, J. G. Schwarz,, F. M. Hashem,, R. C. Whiting,, and K. Yoon. 2009. Development and validation of a predictive model for Listeria monocytogenes Scott A as a function of temperature, pH, and commercial mixture of potassium lactate and sodium diacetate. J. Microbiol. Biotechnol. 19: 718 726.
2. Adams, M. R.,, C. L. Little,, and M. C. Easter. 1991. Modeling the effect of pH, acidulant and temperature on the growth rate of Yersinia enterocolitica. J. Appl. Bacteriol. 71: 65 71.
3. Adekunte, A.,, V. P. Valdramidis,, B. K. Tiwari,, N. Slone,, P. J. Cullen,, C. P. O’Donnell,, and A. Scanell. 2010. Resistance of Cronobacter sakazakii in reconstituted powdered infant formula during ultrasound at controlled temperatures: a quantitative approach on microbial responses. Int. J. Food Microbiol. 142: 53 59.
4. Agresti, A. 2002. Categorical Data Analysis. John Wiley & Sons, New York, NY.
5. Alber, S. A.,, and D. W. Schaffner. 1992. Evaluation of data transformations used with the square root and Schoolfield models for predicting bacterial growth rate. Appl. Environ. Microbiol. 58: 3337 3342.
6. Albert, I.,, and P. Mafart. 2005. A modified Weibull model for bacterial inactivation. Int. J. Food Microbiol. 100: 197 211.
7. Antwi, M.,, A. H. Geeraerd,, K. M. Vereecken,, R. Jenné,, K. Bernaerts,, and J. F. Van Impe. 2006. Influence of a gel microstructure as modified by gelatin concentration on Listeria innocua growth. Innov. Food Sci. Emerg. Technol. 7: 124 131.
8. Antwi, M.,, K. Bernaerts,, J. F. Van Impe,, and A. H. Geeraerd. 2007. Modelling the combined effects of structured food model system and lactic acid on Listeria innocua and Lactococcus lactis growth in mono- and coculture. Int. J. Food Microbiol. 120: 71 84.
9. Arroyo López, F. N.,, M. C. Durán Quintana,, and A. Garrido Fernández. 2007. Modelling of the growth-no growth interface of Issatchenkia occidentalis, an olive spoiling yeast, as a function of the culture media, NaCl, citric and sorbic acid concentrations: study of its inactivation in the no growth region. Int. J. Food Microbiol. 117: 150 159.
10. Arsène, F.,, T. Tomoyasu,, and B. Bukaua. 2000. The heat shock response of Escherichia coli. Int. J. Food Microbiol. 55: 3 9.
11. Augustin, J. C.,, and V. Carlier. 2000. Mathematical modelling of the growth rate and lag time for Listeria monocytogenes. Int. J. Food Microbiol. 56: 29 51.
12. Augustin, J. C.,, and V. Carlier. 2000. Modelling the growth rate of Listeria monocytogenes with a multiplicative type model including interactions between environmental factors. Int. J. Food. Microbiol. 56: 53 70.
13. Augustin, J. C.,, V. Zuliani,, M. Cornu,, and L. Guillier. 2005. Growth rate and growth probability of Listeria monocytogenes in dairy, meat and seafood products in suboptimal conditions. J. Appl. Microbiol. 99: 1019 1042.
14. Babbar, S. B.,, and R. Jain. 2006. Xanthan gum: an economical partial substitute for agar in microbial culture media. Curr. Microbiol. 52: 287 292.
15. Bajard, S.,, L. Rosso,, G. Fardel,, and J. P. Flandrois. 1996. The particular behaviour of Listeria monocytogenes under sub-optimal conditions. Int. J. Food Microbiol. 29: 201 211.
16. Baker, D. A.,, and C. Genigeorgis. 1990. Predicting the safe storage of fresh fish under modified atmospheres with respect to Clostridium botulinum toxigenicity by modeling length of the lag phase of growth. J. Food Prot. 53: 131 140.
17. Bang, W. S.,, H. J. Chung,, S. S. Jin,, T. Ding,, I. G. Hwang,, G. J. Woo,, S. D. Ha,, G. J. Bahk,, and D. H. Oh. 2008. Prediction of Listeria monocytogenes growth kinetics in sausages formulated with antimicrobials as a function of temperature and concentrations. Food Sci. Biotechnol. 17: 1316 1321.
18. Baranyi, J. 1998. Comparison of stochastic and deterministic concepts of bacterial lag. J. Theor. Biol. 192: 403 408.
19. Baranyi, J.,, S. M. George,, and Z. Kutalik. 2009. Parameter estimation for the distribution of single cell lag times. J. Theor. Biol. 259: 24 30.
20. Baranyi, J.,, and T. A. Roberts. 1994. A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23: 277 294.
21. Baranyi, J.,, and T. A. Roberts. 1995. Mathematics of predictive food microbiology. Int. J. Food Microbiol. 26: 199 218.
22. Baranyi, J.,, T. Ross,, T. A. McMeekin,, and T. A. Roberts. 1996. Effects of parametrization on the performance of empirical models used in ‘predictive microbiology’. Food Microbiol. 13: 83 91.
23. Baranyi, J.,, and M. Tamplin. 2004. ComBase: a common database on microbial responses to food environments. J. Food Prot. 67: 1967 1971.
24. Basheer, I. A.,, and M. Hajmeer. 2000. Artificial neural networks: fundamentals, computing, design, and application. J. Microbiol. Methods 43: 3 31.
25. Bermúdez, J.,, D. López,, J. Valls,, and J. Wagensberg. 1989. On the analysis of microbiological processes by Monte Carlo simulation techniques. Comput. Appl. Biosci. 5: 305 312.
26. Bernaerts, K.,, E. Dens,, K. Vereecken,, A. H. Geeraerd,, A. R. Standaert,, F. Devlieghere,, J. Debevere,, and J. F. Van Impe. 2004. Concepts and tools for predictive modeling of microbial dynamics. J. Food Prot. 67: 2041 2052.
27. Bidlas, E.,, and R. J. W. Lambert. 2008. Quantification of hurdles: predicting the combination of effects—interaction vs. non-interaction. Int. J. Food Microbiol. 128: 78 88.
28. Bover-Cid, S.,, N. Belletti,, M. Garriga,, and T. Aymerich. 2011. Model for Listeria monocytogenes inactivation on dry-cured ham by high hydrostatic pressure processing. Food Microbiol. 28: 804 809.
29. Boyle, N. R.,, and J. A. Morgan. 2009. Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii. BMC Syst. Biol. 3: 4.
30. Braun, P.,, and J. P. Sutherland. 2004. Predictive modelling of growth and enzymatic synthesis and activity by a cocktail of Yarrowia lipolytica, Zygosaccharomyces bailii and Pichia anomala. Food Microbiol. 21: 459 467.
31. Brocklehurst, T. F.,, G. A. Mitchell,, and A. C. Smith. 1997. A model experimental surface for the growth of bacteria on foods. Food Microbiol. 14: 303 311.
32. Brul, S.,, F. I. C. Mensonides,, K. J. Hellingwerf,, and M. J. Teixeira de Mattos. 2008. Microbial systems biology: new frontiers open to predictive microbiology. Int. J. Food Microbiol. 128: 16 21.
33. Buchanan, R. L.,, R. C. Whiting,, and W. C. Damert. 1997. When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiol. 14: 313 326.
34. Buchanan, R. L.,, L. K. Bagi,, R. V. Goins,, and J. G. Philips. 1993. Response surface models for the growth kinetics of Escherichia coli O157:H7. Food Microbiol. 10: 303 315.
35. Buchanan, R. L.,, and J. G. Philips. 2000. Updated models for the effects of temperature, initial pH, NaCl, and NaNO 2 on the aerobic and anaerobic growth of Listeria monocytogenes. Quant. Microbiol. 2: 103 128.
36. Burgard, A.,, and C. Maranas. 2002. Optimization-based framework for inferring and testing hypothesized metabolic objective functions. Biotechnol. Bioeng. 82: 670 677.
37. Cerf, O.,, L. R. Davey,, and A. K. Sadoudi. 1996. Thermal inactivation of bacteria—a new predictive model for the combined effect of three environmental factors: temperature, pH and water activity. Food Res. Int. 29: 219 226.
38. Chorin, E.,, D. Thuault,, J. J. Cléret,, and C. M. Bourgeois. 1997. Modelling Bacillus cereus growth. Int. J. Food Microbiol. 38: 229 334.
39. Chung, H.,, W. Bang,, and M. Drake. 2006. Stress response of Escherichia coli. Compr. Rev. Food Sci. F 5: 52 64.
40. Cole, M. B.,, M. V. Jones,, and C. Holyoak. 1990. The effect of pH, salt concentration and temperature on the survival and growth of Listeria monocytogenes. J. Appl. Bacteriol. 69: 63 72.
41. Coroller, L.,, V. Guerrot,, V. Huchet,, Y. Le Marc,, P. Mafart,, D. Sohier,, and D. Thuault. 2005. Modelling the influence of single acid and mixture on bacterial growth. Int. J. Food Microbiol. 100: 167 178.
42. Covert, M.,, C. Schilling,, and B. Palsson. 2001. Regulation of gene expression in flux balance models of metabolism. J. Theor. Biol. 213: 309 325.
43. Cuppers, H. G. A. M.,, S. Oomes,, and S. Brul. 1997. A model for the combined effects of temperature and salt concentration on growth rate of food spoilage molds. Appl. Environ. Microbiol. 63: 3764 3769.
44. Dalgaard, P. 1995. Modelling of microbial activity and prediction of shelf life for packed fresh fish. Int. J. Food Microbiol. 26: 305 317.
45. Dalgaard, P.,, O. Mejlholm,, and H. H. Huss. 1997. Application of an iterative approach for development of a microbial model predicting the shelf-life of packed fish. Int. J. Food Microbiol. 38: 169 179.
46. Dantigny, P.,, and M. Bensoussan. 2008. The logarithmic transformation should be avoided for stabilising the variance of mould growth rate. Int. J. Food Microbiol. 121: 225 228.
47. Daughtry, G. J.,, K. R. Davey,, and K. D. King. 1997. Temperature dependence of growth kinetics of food bacteria. Food Microbiol. 14: 21 30.
48. Davey, K. R. 1993. Extension of the generalized chart for combined temperature and pH. LWT Food Sci. Technol. 26: 476 479.
49. Delignette-Muller, M. L.,, M. Cornu,, R. Pouillot,, and J. B. Denis. 2006. Use of Bayesian modelling in risk assessment: application to growth of Listeria monocytogenes and food flora in cold-smoked salmon. Int. J. Food Microbiol. 106: 195 208.
50. denBesten, H. M. W.,, C. J. Ingham,, J. E. T. van Hylckama Vlieg,, M. M. Beerthuyzen,, M. H. Zwietering,, and T. Abee. 2007. Quantitative analysis of population heterogeneity of the adaptive salt stress response and growth capacity of Bacillus cereus ATCC 14579. Appl. Environ. Microbiol. 73: 4797 4804.
51. Dens, E.,, and J. Van Impe. 2001. On the need for another type of predictive models in structured foods. Int. J. Food Microbiol. 64: 247 260.
52. Dens, E. J.,, K. Bernaerts,, A. R. Standaert,, J.-U. Kreft,, and J. F. Van Impe. 2005. Cell division theory and individual-based modeling of microbial lag. Part II. Modeling lag phenomena induced by temperature shifts. Int. J. Food Microbiol. 101: 319 332.
53. Dens, E. J.,, K. Bernaerts,, A. R. Standaert,, and J. F. Van Impe. 2005. Cell division theory and individual-based modeling of microbial lag. Part I. The theory of cell division. Int. J. Food Microbiol. 101: 303 318.
54. Devlieghere, F.,, A. H. Geeraerd,, K. J. Versyck,, H. Bernaert,, J. F. Van Impe,, and J. Debevere. 2000. Shelf life of modified atmosphere packed cooked meat products: addition of Na-lactate as a fourth shelf life determinative factor in a model and product validation. Int. J. Food Microbiol. 58: 93 106.
55. Dhar, N.,, and J. D. McKinney. 2007. Microbial phenotypic heterogeneity and antibiotic tolerance. Curr. Opin. Microbiol. 10: 30 38.
56. Ding, T.,, Q. L. Dong,, S. M. E. Rahman,, and D. H. Oh. 2011. Response surface modeling of Listeria monocytogenes inactivation on lettuce treated with electrolyzed oxidizing water. J. Food Process Eng. 34: 1729 1745.
57. Dodds, K. L. 1989. Combined effect of water activity and pH on inhibition of toxin production by Clostridium botulinum in cooked, vacuum-packed potatoes. Appl. Environ. Microbiol. 55: 656 660.
58. Dong, Q.,, K. Tu,, L. Guo,, H. Li,, and Y. Zhao. 2007. Response surface model for prediction of growth parameters from spores of Clostridium sporogenes under different experimental conditions. Food Microbiol. 24: 624 632.
59. Donsì, G.,, G. Ferrari,, and P. Maresca. 2003. On the modelling of the inactivation kinetics of Saccharomyces cerevisiae by means of combined temperature and high pressure treatments. Innov. Food Sci. Emerg. Technol. 4: 35 44.
60. Esnoz, A.,, P. M. Periago,, R. Conesa,, and A. Palop. 2006. Application of artificial neural networks to describe the combined effect of pH and NaCl on the heat resistance of Bacillus stearothermophilus. Int. J. Food Microbiol. 106: 153 158.
61. Fernández-Navarro F.,, A. Valero,, C. Hervás-Martínez,, P. A. Gutiérrez,, R. A. García-Gimeno,, and G. Zurera-Cosano. 2010. Development of a multi-classification neural network model to determine the microbial growth/no growth interface. Int. J. Food Microbiol. 141: 203 212.
62. Ferrer, J.,, C. Prats,, D. Lopez,, and J. Vives-Rego. 2009. Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis. Int. J. Food Microbiol. 134: 2 8.
63. Francois, K.,, F. Devlieghere,, M. Uyttendaele,, A. R. Standaert,, A. H. Geeraerd,, P. Nadal,, J. F. Van Impe,, and J. Debevere. 2006. Single cell variability of L. monocytogenes grown on liver paté and cooked ham at 7°C: comparing challenge test data to predictive simulations. J. Appl. Microbiol. 100: 800 812.
64. Fujikawa, H.,, and T. Itoh. 1996. Tailing of thermal inactivation curve of Aspergillus niger spores. Appl. Environ. Microbiol. 62: 3745 3749.
65. Gaillard, S.,, I. Leguérinel,, and P. Mafart. 1998. Model for combined effects of temperature, pH and water activity on thermal inactivation of Bacillus cereus spores. J. Food Sci. 63: 887 889.
66. Garcia, D.,, A. J. Ramos,, V. Sanchis,, and S. Marín. 2009. Predicting mycotoxins in foods: a review. Food Microbiol. 26: 757 769.
67. García-Gimeno, R. M.,, C. Hervás-Martínez,, E. Barco-Alcalá,, G. Zurera-Cosano,, and E. Sanz-Tapia. 2003. An artificial neural network approach to Escherichia coli O157:H7 growth estimation. J. Food Sci. 68: 639 645.
68. García-Gimeno, R. M.,, C. Hervás-Martínez,, R. Rodríguez-Pérez,, and G. Zurera-Cosano. 2005. Modelling the growth of Leuconostoc mesenteroides by artificial neural networks. Int. J. Food Microbiol. 105: 317 332.
69. Geeraerd, A.,, C. Herremans,, C. Cenens,, and J. F. Van Impe. 1998. Application of artificial neural networks as a non-linear modular modeling technique to describe bacterial growth in chilled food products. Int. J. Food Microbiol. 44: 49 68.
70. Geeraerd, A. H.,, C. H. Herremans,, and J. F. Van Impe. 2000. Structural model requirements to describe microbial inactivation during a mild heat treatment. Int. J. Food Microbiol. 59: 185 209.
71. Geeraerd, A. H.,, V. P. Valdramidis,, F. Devlieghere,, H. Bernaert,, J. Debevere,, and J. F. Van Impe. 2004. Development of a novel approach for secondary modelling in predictive microbiology: incorporation of microbiological knowledge in black box polynomial modelling. Int. J. Food Microbiol. 91: 229 244.
72. Geeraerd, A. H.,, V. P. Valdramidis,, and J. F. Van Impe. 2005. GInaFiT, a freeware tool to assess non-log-linear microbial survivor curves. Int. J. Food Microbiol. 102: 95 105.
73. Ghanou Besse, N.,, N. Audinet,, L. Barre,, A. Cauquil,, M. Cornu,, and P. Colin. 2006. Effect of the inoculum size on Listeria monocytogenes growth in structured media. Int. J. Food Microbiol. 110: 43 51.
74. Gil, M. M.,, T. R. S. Brandão,, and C. L. M. Silva. 2006. A modified Gompertz model to predict microbial inactivation under time-varying temperature conditions. J. Food Eng. 76: 89 94.
75. Ginovart, M.,, and J. C. Canadas. 2008. INDISIM-YEAST: an individual-based simulator on a website for experimenting and investigating diverse dynamics of yeast populations in liquid media. J. Ind. Microbiol. Biot. 35: 1359 1366.
76. Ginovart, M.,, D. López,, and A. Gras. 2005. Individual-based modelling of microbial activity study mineralization of C and N and nitrification process in soil. Nonlinear Anal. Real World Appl. 6: 773 795.
77. Ginovart, M.,, D. López,, and J. Valls. 2002. INDISIM, an individual-based discrete simulation model to study bacterial cultures. J. Theor. Biol. 214: 305 319.
78. Ginovart, M.,, C. Prats,, X. Portell,, and M. Silbert. 2011. Exploring the lag phase and growth initiation of a yeast culture by means of an individual-based model. Food Microbiol. 28: 810 817.
79. Giuffrida, A.,, D. Valenti,, G. Ziino,, B. Spagnolo,, and A. Panebianco. 2009. A stochastic interspecific competition model to predict the behaviour of Listeria monocytogenes in the fermentation process of a traditional Sicilian salami. Eur. Food Res. Technol. 228: 767 775.
80. Grijspeerdt, K.,, J.-U. Kreft,, and W. Messens. 2005. Individual-based modelling of growth and migration of Salmonella enteritidis in hens’ eggs. Int. J. Food Microbiol. 100: 323 333.
81. Grimm, V.,, T. Wyszomirski,, D. Aikman,, and J. Uchmanski. 1999. Individual based modelling and ecological theory: synthesis of a workshop. Ecol. Model. 115: 275 282.
82. Guillier, L.,, V. Stahl,, B. Hezard,, E. Notz,, and R. Briandet. 2008. Modelling the competitive growth between Listeria monocytogenes and biofilm microflora of smear cheese wooden shelves. Int. J. Food Microbiol. 128: 51 57.
83. Gunvig, A.,, J. Blom-Hanssen,, T. Jacobsen,, F. Hansen,, and C. Borggaard. 2007. A predictive model for growth of Listeria monocytogenes in meat products with seven hurdle variables, p. 197 200. In Proceedings of the 5th International Conference on Predictive Modelling in Foods. Agricultural University of Athens, Athens, Greece.
84. Gysemans, K. P. M.,, K. Bernaerts,, A. Vermeulen,, A. H. Geeraerd,, J. Debevere,, F. Devlieghere,, and J. F. Van Impe. 2007. Exploring the performance of logistic regression model types on growth/no growth data of Listeria monocytogenes. Int. J. Food Microbiol. 114: 316 331.
85. Hajmeer, M. N.,, and I. A. Basheer. 2003. A hybrid Bayesian-neural network approach for probabilistic modeling of bacterial growth/no-growth interface. Int. J. Food Microbiol. 82: 233 243.
86. Hajmeer, M.,, and I. Basheer. 2002. A probabilistic neural network approach for modeling and classification of bacterial growth/no-growth data. J. Microbiol. Methods 51: 217 226.
87. Hajmeer, M.,, I. Basheer,, and D. O. Cliver. 2006. Survival curves of Listeria monocytogenes in chorizos modeled with artificial neural networks. Food Microbiol. 23: 561 570.
88. Härdin, H.,, and J. van Schuppen. 2006. System reduction ofnonlinear positive systems by linearization and truncation, p. 431 438. In Positive Systems—Proceedings of the Second International Multidisciplinary Symposium on Positive Systems: Theory and Applications. Lecture Notes in Control and Information Sciences, vol. 341. Springer, Berlin, Germany.
89. Hills, B.,, and K. Wright. 1994. A new model for bacterial growth in heterogeneous systems. J. Theor. Biol. 168: 31 41.
90. Hinshelwood, C. N. 1947. The Chemical Kinetics of the Bacterial Cell. Clarendon Press, Oxford, England.
91. Ho, S. Y.,, and G. S. Mittal. 2001. Non-thermal microbial inactivation in waste brine using high-voltage low-energy electrical pulses. Innov. Food Sci. Emerg. Technol. 2: 251 259.
92. Holzhütter, H.-G. 2004. The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. Eur. J. Biochem. 271: 2905 2922.
93. Hom, L. W. 1972. Kinetics of chlorine disinfection in an ecosystem. J. Sanitary Eng. Div. 98: 183 194.
94. Hotchin, J. E. 1955. Use of methyl cellulose as substitute for agar in tissue-culture overlays. Nature 175: 352 355.
95. Houtsma, P. C.,, M. L. Kant-Muermans,, F. M. Rombouts,, and M. H. Zwietering. 1996. Model for the combined effects of temperature, pH, and sodium lactate on growth rates of Listeria innocua in broth and bologna-type sausages. Appl. Environ. Microbiol. 62: 1616 1622.
96. Hülsheger, H.,, J. Potel,, and E.-G. Niemann. 1981. Killing of bacteria with electric pulses of high field strength. Radiat. Environ. Biophys. 20: 53 65.
97. Hwang, C. A.,, and M. L. Tamplin. 2005. Modeling the lag phase and growth rate of Listeria monocytogenes in ground ham containing sodium lactate and sodium diacetate at various storage temperatures. J. Food Sci. 72: M246 M253.
98. Janssen, M.,, A. H. Geeraerd,, F. Logist,, Y. De Visscher,, K. M. Vereecken,, J. Debevere,, F. Devlieghere,, and J. F. Van Impe. 2006. Modelling Yersinia enterocolitica inactivation in coculture experiments with Lactobacillus sakei as based on pH and lactic acid profiles. Int. J. Food Microbiol. 111: 59 72.
99. Jeanson, S.,, J. Chadoeuf,, M. N. Madec,, S. Aly,, J. Floury,, T. F. Brocklehurst,, and S. Lortal. 2011. Spatial distribution of bacterial colonies in a model cheese. Appl. Environ. Microbiol. 77: 1493 1500.
100. Jeyamkondan, S.,, D. S. Jayas,, and R. A. Holley. 2001. Microbial growth modelling with artificial neural networks. Int. J. Food Microbiol. 64: 343 354.
101. Koutsoumanis, K. P.,, P. A. Kendall,, and J. N. Sofos. 2004. A comparative study on growth limits of Listeria monocytogenes as affected by temperature, pH and a w when grown in suspension or on a solid surface. Food Microbiol. 21: 415 422.
102. Kreft, J.-U.,, G. Booth,, and J. W. T. Wimpenny. 1998. BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144: 3275 3287.
103. Kreft, J. U.,, C. Picioreanu,, J. W. T. Wimpenny,, and M. C. M. Van Loosdrecht. 2001. Individual-based modeling of biofilm. Microbiology 147: 2897 2912.
104. Leistner, L. 2000. Basic aspects of food preservation by hurdle technology. Int. J. Food Microbiol. 55: 181 186.
105. Le Marc, Y.,, V. Huchet,, C. M. Bourgeois,, J. P. Guyonnet,, P. Mafart,, and D. Thuault. 2002. Modelling the growth kinetics of Listeria as a function of temperature, pH and organic acid concentration. Int. J. Food Microbiol. 73: 219 237.
106. Le Marc, Y.,, L. Valik,, and A. Medvedova. 2009. Modelling the effect of the starter culture on the growth of Staphylococcus aureus in milk. Int. J. Food Microbiol. 129: 306 311.
107. Leporq, B.,, J.-M. Membré,, C. Dervin,, P. Buche,, and J. P. Guyonnet. 2005. The ‘Sym’Previus’ software, a tool to support decisions to the foodstuff safety. Int. J. Food Microbiol. 100: 231 237.
108. Leroy, F.,, B. Degeest,, and L. De Vuyst. 2002. A novel area of predictive modelling: describing the functionality of beneficial microorganisms in foods. Int. J. Food Microbiol. 73: 251 259.
109. Li, H.,, G. Xie,, and A. Edmondson. 2007. Evolution and limitations of primary mathematical models in predictive microbiology. Br. Food J. 109: 608 626.
110. Liebermeister, W.,, U. Bauer,, and E. Klipp. 2005. Biochemical network models simplified by balanced truncation. FEBS J. 272: 4034 4043.
111. Lindroth, S. E.,, and C. A. Genigeorgis. 1986. Probability of growth and toxin production by nonproteolytic Clostridium botulinum in rockfish stored under modified atmospheres. Int. J. Food Microbiol. 3: 167 181.
112. Llaneras, F.,, and J. Picó. 2008. Stoichiometric modelling of cell metabolism. J. Biosci. Bioeng. 105: 1 11.
113. Mafart, P.,, and I. Leguérinel. 1998. Modeling combined effects of temperature and pH on heat resistance of spores by a linear-Bigelow equation. J. Food Sci. 63: 6 8.
114. Malakar, P. K.,, G. C. Barker,, M. H. Zwietering,, and K. van ’t Riet. 2003. Relevance of microbial interactions to predictive microbiology. Int. J. Food Microbiol. 84: 263 272.
115. McClure, P. J.,, T. M. Kelly,, and T. A. Roberts. 1991. The effects of temperature, pH, sodium chloride and sodium nitrite on the growth of Listeria monocytogenes. Int. J. Food Microbiol. 14: 77 92.
116. McKellar, R. 2001. Development of a dynamic continuous-discrete-continuous model describing the lag phase of individual bacterial cells. J. Appl. Microbiol. 90: 407 413.
117. McKellar, R. C. 1997. A heterogeneous population model for the analysis of bacterial growth kinetics. Int. J. Food Microbiol. 36: 179 186.
118. McMeekin, T. A.,, J. Bowman,, O. McQuestin,, L. Mellefont,, T. Ross,, and M. Tamplin. 2008. The future of predictive microbiology: strategic research, innovative applications and great expectations. Int. J. Food Microbiol. 128: 2 9.
119. McMeekin, T. A.,, R. E. Chandler,, and P. E. Doe. 1987. Model for combined effect of temperature and salt concentration/water activity on the growth rate of Staphylococcus xylosus. J. Appl. Bacteriol. 62: 543 550.
120. McMeekin, T. A.,, J. N. Olley,, T. Ross,, and D. A. Ratkowsky. 1993. Predictive Microbiology: Theory and Application. Research Studies Press Ltd., Baldock, England.
121. McMeekin, T. A.,, J. Olley,, D. A. Ratkowsky,, and T. Ross. 2002. Predictive microbiology: towards the interface and beyond. Int. J. Food Microbiol. 73: 395 407.
122. McMeekin, T. A.,, and T. Ross. 2002. Predictive microbiology: providing a knowledge-based framework for change management. Int. J. Food Microbiol. 78: 133 153.
123. Mejlholm, O.,, and P. Dalgaard. 2007. Modeling and predicting the growth of lactic acid bacteria in lightly preserved seafood and their inhibiting effect on Listeria monocytogenes. J. Food Prot. 70: 2485 2497.
124. Mejlholm, O.,, and P. Dalgaard. 2009. Development and validation of an extensive growth and growth boundary model for Listeria monocytogenes in lightly preserved and ready-to-eat shrimp. J. Food Prot. 72: 2132 2143.
125. Mejlholm, O.,, A. Gunvig,, C. Borggaard,, J. Blom-Hanssen,, L. Mellefont,, T. Ross,, F. Leroi,, T. Else,, D. Visser,, and P. Dalgaard. 2010. Predicting growth rates and growth boundary of Listeria monocytogenes—an international validation study with focus on processed and ready-to-eat meat and seafood. Int. J. Food Microbiol. 141: 137 150.
126. Meldrum, R. J.,, T. F. Brocklehurst,, D. R. Wilson,, and P. D. G. Wilson. 2003. The effects of cell immobilization, pH, and sucrose on the growth of Listeria monocytogenes Scott A at 10°C. Food Microbiol. 20: 97 103.
127. Membré, J. M.,, and R. J. W. Lambert. 2008. Application of predictive modelling techniques in industry: from food design up to risk assessment. Int. J. Food Microbiol. 128: 10 15.
128. Mertens, L.,, A. H. Geeraerd,, T. D. T. Dang,, A. Vermeulen,, K. Serneels,, E. Van Derlinden,, A. M. Cappuyns,, P. Moldenaers,, J. Debevere,, F. Devlieghere,, and J. F. Van Impe. 2009. Design of an experimental viscoelastic food model system for studying Zygosaccharomyces bailii spoilage in acidic sauces. Appl. Environ. Microbiol. 75: 7060 7069.
129. Mertens, L.,, E. Van Derlinden,, T. D. T. Dang,, A. M. Cappuyns,, A. Vermeulen,, J. Debevere,, P. Moldenaers,, F. Devlieghere,, A. H. Geeraerd,, and J. F. Van Impe. 2011. On the critical evaluation of growth/no growth assessment of Zygosaccharomyces bailii with optical density measurements: liquid versus structured media. Food Microbiol. 28: 736 745.
130. Métris, A.,, Y. Le Marc,, A. Elfwing,, A. Ballagi,, and J. Baranyi. 2005. Modelling the variability of lag times and the first generation times of single cells of E. coli. Int. J. Food Microbiol. 100: 13 19.
131. Miles, D. W.,, T. Ross,, J. Olley,, and T. A. McMeekin. 1997. Development and evaluation of a predictive model for the effect of temperature and water activity on the growth rate of Vibrio parahaemolyticus. Int. J. Food Microbiol. 38: 133 142.
132. Molina, M.,, and L. Giannuzzi. 1999. Combined effect of temperature and propionic acid concentration on the growth of Aspergillus parasiticus. Food Res. Int. 32: 677 682.
133. Murphy, J. T.,, and R. Walshe. 2007. Micro-gen: an agent-based model of bacteria-antibiotic interactions in batch culture, p. 239 242. In Proceedings of the Annual European Simulation and Modelling (ESM 2007). Eurosis, Ostend, Belgium.
134. Nene, Y. L.,, V. K. Sheila,, and J. P. Moss. 1996. Tapioca—a potential substitute for agar in tissue culture media. Curr. Sci. 70: 493 494.
135. Nikolaou, M.,, and V. H. Tam. 2005. A new modeling approach to the effect of antimicrobial agents on heterogeneous microbial populations. J. Math. Biol. 52: 154 182.
136. Nilsson, L.,, and Y. Chen,, M. L. Chikindas,, H. H. Huss,, L. Gram,, and T. J. Montville. 2000. Carbon dioxide and nisin act synergistically on Listeria monocytogenes. Appl. Environ. Microbiol. 66: 769 774.
137. Noma, S.,, D. Kajiyama,, N. Igura,, M. Shimoda,, and I. Hayakawa. 2006. Mechanisms behind tailing in the pressure inactivation curve of a clinical isolate of Escherichia coli O157:H7. Int. J. Food Microbiol. 109: 103 108.
138. Noriega, E.,, A. Laca,, and M. Díaz. 2009. Listeria growth under diffusional limitations in synthetic meats. Int. J. Food Sci. Technol. 44: 725 734.
139. Nyström, T. 2004. Stationary-phase physiology. Annu. Rev. Microbiol. 58: 161 181.
140. Parente, E.,, M. A. Giglio,, A. Ricciardi,, and F. Clementi. 1998. The combined effect of nisin, leucocin F10, pH, NaCl and EDTA on the survival of Listeria monocytogenes in broth. Int. J. Food Microbiol. 40: 65 75.
141. Park, S. Y.,, J. W. Choi,, J. Yeon,, M. Jeong Lee,, D. H. Chung,, M. G. Kim,, K. H. Lee,, K. S. Kim,, D. H. Lee,, G. J. Bahk,, D. H. Bae,, K. Y. Kim,, C. H. Kim,, and S. D. Ha. 2009. Predictive modeling for the growth of Listeria monocytogenes as a function of temperature, NaCl and pH. J. Microbiol. Biotechnol. 15: 1323 1329.
142. Peck, S. L. 2004. Simulation as experiment: a philosophical reassessment for biological modeling. Trends Ecol. Evol. 19: 530 534.
143. Peleg, M. 1995. A model for microbial survival after exposure to pulsed electric field. J. Sci. Food Agric. 67: 93 99.
144. Peleg, P.,, M. D. Normand,, and E. Damru. 1997. Mathematical interpretation of dose-response curves. Bull. Math. Biol. 59: 747 761.
145. Pin, C.,, J. Sutherland,, and J. Baranyi. 1999. Validating predictive models of food spoilage organisms. J. Appl. Microbiol. 87: 491 499.
146. Poschet, F.,, K. M. Vereecken,, A. H. Geeraerd,, B. M. Nicolaï,, and J. F. Van Impe. 2005. Analysis of a novel class of predictive microbial growth models and application to coculture growth. Int. J. Food Microbiol. 100: 107 124.
147. Prats, C.,, D. López,, A. Giró,, J. Ferrer,, and J. Valls. 2006. Individual-based modelling of bacterial cultures to study the microscopic causes of the lag phase. J. Theor. Biol. 241: 939 953.
148. Prats, C.,, A. Giró,, J. Ferrer,, D. López,, and J. Vives-Rego. 2008. Analysis and IbM simulation of the stages in bacterial lag phase: basis for an updated definition. J. Theor. Biol. 252: 56 68.
149. Presser, K. A.,, D. A. Ratkowsky,, and T. Ross. 1997. Modelling the growth rate of Escherichia coli as a function of pH and lactic acid concentration. Appl. Environ. Microbiol. 63: 2355 2360.
150. Presser, K. A.,, T. Ross,, and D. A. Ratkowsky. 1998. Modelling the growth limits (growth/no growth interface) of Escherichia coli as a function of temperature, pH, lactic acid concentration, and water activity. Appl. Environ. Microbiol. 64: 1773 1779.
151. Ramakrishna, R.,, J. S. Edwards,, A. Mcculluch,, and B. O. Palsson. 2001. Flux balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometric constraints. Am. J. Physiol. Regul. Integr. Comp. Physiol. 280: R695 R704.
152. Ratkowsky, D. A.,, R. K. Lowry,, T. A. McMeekin,, A. N. Stokes,, and E. Chandler. 1983. Model for bacterial culture growth rate throughout the entire biokinetic temperature range. J. Bacteriol. 154: 1222 1226.
153. Ratkowsky, D. A.,, J. Olley,, T. A. McMeekin,, and A. Ball. 1982. Relationship between temperature and growth rate of bacterial cultures. J. Bacteriol. 149: 1 5.
154. Ratkowsky, D. A.,, and T. Ross. 1995. Modelling the bacterial growth/no growth interface. Lett. Appl. Microbiol. 20: 29 33.
155. Razavilar, V.,, and C. Genigeorgis. 1998. Prediction of Listeria spp. growth as affected by various levels of chemicals, pH, temperature and storage time in a model broth. Int. J. Food Microbiol. 40: 149 157.
156. Ross, T.,, D. A. Ratkowsky,, L. A. Mellefont,, and T. A. McMeekin. 2003. Modelling the effects of temperature, water activity, pH and lactic acid concentration on the growth rate of Escherichia coli. Int. J. Food Microbiol. 82: 33 43.
157. Ross, T.,, and J. Sumner. 2002. A simple, spreadsheet-based, food safety risk assessment tool. Int. J. Food Microbiol. 77: 39 53.
158.Rosso, L. 1995. Modélisation et microbiologie prévisionnelle: elaboration d’un nouvel outil pour l’agroalimentaire. Ph.D. thesis. Université Claude Bernard, Lyon, France.
159. Rosso, L.,, J. R. Lobry,, S. Bajard,, and J. P. Flandrois. 1995. Convenient model to describe the combined effects of temperature and pH on microbial growth. Appl. Environ. Microbiol. 61: 610 616.
160. Rosso, L.,, J. R. Lobry,, and J. P. Flandrois. 1993. An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. J. Theor. Biol. 162: 447 463.
161. Rosso, L.,, and T. Robinson. 2001. A cardinal model to describe the effect of water activity on the growth of moulds. Int. J. Food Microbiol. 63: 265 273.
162. Salter, M. A.,, D. A. Ratkowsky,, T. Ross,, and T. A. McMeekin. 2000. Modelling the combined temperature and salt (NaCl) limits for growth of a pathogenic Escherichia coli strain using nonlinear logistic regression. Int. J. Food Microbiol. 61: 159 167.
163. Sautour, M.,, P. Dantigny,, C. Divies,, and M. Bensoussan. 2001. A temperature type model for describing the relationship between fungal growth and water activity. Int. J. Food Microbiol. 67: 63 69.
164. Schaffner, D. W.,, W. H. Ross,, and T. J. Montville. 1998. Analysis of the influence of environmental parameters on Clostridium botulinum time-to-toxicity by using three modeling approaches. Appl. Environ. Microbiol. 64: 4416 4422.
165. Schilling, C.,, M. Covert,, I. Famili,, G. Church,, J. Edwards,, and B. Palsson. 2002. Genome-scale metabolic model of Helicobacter pylori 26695. J. Bacteriol. 184: 4582 4593.
166. Schoolfield, R. M.,, P. J. H. Sharpe,, and C. E. Magnuson. 1981. Non linear regression of biological temperature-dependent rate models based on absolute reaction rate theory. J. Theor. Biol. 88: 719 731.
167. Schuetz, R.,, L. Kuepfer,, and U. Sauer. 2007. Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Mol. Syst. Biol. 3: 119.
168. Schuytser, M. A.,, J. Straatsma,, P. M. Keijzer,, M. Verschueren,, and P. De Jong. 2008. A new web-based modelling tool (Websim-MILQ) aimed at optimisation of thermal treatments in the dairy industry. Int. J. Food Microbiol. 128: 153 157.
169. Schvartzman, M. S.,, X. Belessi,, F. Butler,, P. Skandamis,, and K. Jordan. 2010. Comparison of growth limits of Listeria monocytogenes in milk, broth and cheese. J. Appl. Microbiol. 109: 1790 1799.
170. Shamsi, K.,, C. Versteeg,, F. Sherkat,, and J. Wan. 2008. Alkaline phosphatase and microbial inactivation by pulsed electric field in bovine milk. Innov. Food Sci. Emerg. Technol. 9: 217 233.
171. Shimizu, H.,, Y. Shinfuku,, M. Sono,, C. Furusawa,, and T. Hirasawa. 2008. Metabolic flux balance analysis of an industrially useful microorganism Corynebacterium glutamicum by a genome-scale reconstructed model. In Proceedings of the 3rd International Conference on Bio-Inspired Models of Network, Information and Computing Systems, article no. 17. ICST, Brussels, Belgium.
172. Skandamis, P. N.,, and G. J. E. Nychas. 2000. Development and evaluation of a model predicting the survival of Escherichia coli O157:H7 NCTC 12900 in homemade eggplant salad at various temperatures, pHs, and oregano essential oil concentrations. Appl. Environ. Microbiol. 66: 1646 1653.
173. Skandamis, P. N.,, K. W. Davies,, P. J. McClure,, K. Koutsoumanis,, and C. Tassou. 2002. A vitalistic approach for non-thermal inactivation of pathogens in traditional greek salads. Food Microbiol. 19: 405 421.
174. Skandamis, P. N.,, T. F. Brocklehurst,, E. Z. Panagou,, and G. J. E. Nychas. 2007. Image analysis as a mean to model growth of Escherichia coli O157:H7 in gel cassettes. J. Appl. Microbiol. 103: 937 947.
175. Standaert, A. R.,, F. Poschet,, A. H. Geeraerd,, F. V. Uylbak,, J. U. Kreft,, and J. F. Van Impe. 2004. A novel class of predictive microbial growth models: implementation in an individual-based framework, p. 183 188. In Proceedings of the 9th International Symposium on Computer Applications in Biotechnology (CAB9).
176. Stecchini, M. L.,, M. Del Torre,, I. Sarais,, O. Saro,, M. Messina,, and E. Maltini. 1998. Influence of structural properties and kinetic constraints on Bacillus cereus growth. Appl. Environ. Microbiol. 64: 1075 1078.
177. Swinnen, I. A. M.,, K. Bernaerts,, K. Gysemans,, and J. F. Van Impe. 2005. Quantifying microbial lag phenomena due to a sudden rise in temperature: a systematic macroscopic study. Int. J. Food Microbiol. 100: 85 96.
178. Tapia deDaza, M. S.,, Y. Villegas,, and A. Martinez. 1991. Minimal water activity for growth of Listeria monocytogenes as affected by solute and temperature. Int. J. Food Microbiol. 14: 333 337.
179. Theys, T. E.,, A. H. Geeraerd,, A. Verhulst,, K. Poot,, F. Van Bree,, F. Devlieghere,, P. Moldenaers,, D. Wilson,, T. Brocklehurst,, and J. F. Van Impe. 2008. Effect of pH, water activity and gel microstructure including oxygen profiles and rheological characterization, on the growth kinetics of Salmonella Typhimurium. Int. J. Food Microbiol. 128: 67 77.
180. Theys, T. E.,, A. H. Geeraerd,, and J. F. Van Impe. 2009. Evaluation of a mathematical model structure describing the effect of (gel) structure on the growth of Listeria innocua, Lactococcus lactis and Salmonella Typhimurium. J. Appl. Microbiol. 107: 775 784.
181. Theys, T. E.,, A. H. Geeraerd,, F. Devlieghere,, and J. F. Van Impe. 2009. Extracting information on the evolution of living- and dead-cell fractions of Salmonella Typhimurium colonies in gelatin gels based on microscopic images and plate-count data. Lett. Appl. Microbiol. 49: 39 45.
182. Theys, T. E.,, A. H. Geeraerd,, F. Devlieghere,, and J. F. Van Impe. 2010. On the selection of relevant environmental factors to predict microbial dynamics in solidified media. Food Microbiol. 27: 220 228.
183. Tienungoon, S.,, D. A. Ratkowsky,, T. A. McMeekin,, and T. Ross. 2000. Growth limits of Listeria monocytogenes as a function of temperature, pH, NaCl, and lactic acid. Appl. Environ. Microbiol. 66: 4979 4987.
184. Tsigarida, E.,, I. Boziaris,, and G. J. E. Nychas. 2003. Bacterial synergism or antagonism in a gel cassette system. Appl. Environ. Microbiol. 69: 7204 7209.
185. Valdramidis, V. P.,, A. H. Geeraerd,, and J. F. Van Impe. 2007. Stress-adaptive responses by heat under the microscope of predictive microbiology. J. Appl. Microbiol. 103: 1922 1930.
186. Valero, A.,, E. Carrasco,, F. Pérez-Rodriguez,, R. M. García-Gimeno,, and G. Zurera. 2006. Growth/no growth model of Listeria monocytogenes as a function of temperature, pH, citric acid and ascorbic acid. Eur. Food Res. Technol. 224: 91 100.
187. VanBreusegem, V.,, and G. Bastin. 1991. Reduced order dynamical modelling of reaction systems: a singular perturbation approach, p. 1049 1054. In Proceedings of the 30th IEEE conference on decision and control. IEEE, Washington, DC.
188. Van Derlinden, E.,, K. Bernaerts,, and J. F. Van Impe. 2009. Unraveling E. coli dynamics close to the maximum growth temperature through heterogeneous modeling. Lett. Appl. Microbiol. 49: 659 665.
189. Van Derlinden, E.,, K. Bernaerts,, and J. F. Van Impe. 2010. Quantifying the heterogeneous heat response of E. coli under dynamic temperatures. J. Appl. Microbiol. 108: 1123 1135.
190. Van Impe, J. F.,, A. M. Cappuyns,, and E. Van Derlinden. 2009. Towards a next generation of predictive models based on systems biology tools. In Proceedings of the 6th International Conference on Predictive Modelling in Foods. ICPMF, Dublin, Ireland.
191. Van Impe, J. F.,, F. Poschet,, A. H. Geeraerd,, and K. M. Vereecken. 2005. Towards a novel class of predictive microbial growth models. Int. J. Food Microbiol. 100: 97 105.
192. Varma, A.,, B. Boesch,, and B. Palsson. 1993. Biochemical production capabilities of Escherichia coli. Biotechnol. Bioeng. 42: 59 73.
193. Vereecken, K. M.,, and J. F. Van Impe. 2002. Analysis and practical implementation of a model for combined growth and metabolite production of lactic acid bacteria. Int. J. Food Microbiol. 73: 239 250.
194. Vereecken, K. M.,, F. Devlieghere,, A. Bockstaele,, J. Debevere,, and J. F. Van Impe. 2003. A model for lactic acid-induced inhibition of Yersinia enterocolitica in mono- and coculture with Lactobacillus sakei. Food Microbiol. 20: 701 713.
195. Vermeulen, A.,, K. P. M. Gysemans,, K. Bernaerts,, A. H. Geeraerd,, J. Debevere,, F. Devlieghere,, and J. F. Van Impe. 2009. Modelling the influence of the inoculation level on the growth/no growth interface of Listeria monocytogenes as a function of pH, a w and acetic acid. Int. J. Food Microbiol. 135: 83 89.
196. Virto, R.,, D. Sanz,, I. Álvarez,, S. Condón,, and J. Raso. 2006. Application of the Weibull model to describe inactivation of Listeria monocytogenes and Escherichia coli by citric and lactic acid at different temperatures. J. Sci. Food Agric. 86: 865 870.
197. Watson, H. E. 1908. A note on the variation of the rate of disinfection with change in the concentration of the disinfectant. J. Hyg. 8: 536 542.
198. Wilson, P. D. G.,, T. F. Brocklehurst,, S. Arino,, D. Thuault,, M. Jakobsen,, M. Lange,, J. Farkas,, J. W. T. Wimpenny,, and J. F. Van Impe. 2002. Modelling microbial growth in structured foods: towards a unified approach. Int. J. Food Microbiol. 73: 275 289.
199. Whiting, R. 1993. Modeling bacterial survival in unfavorable environments. J. Ind. Microbiol. 12: 240 246.
200. Xavier, J. B.,, M. K. De Kreuk,, C. Picioreanu,, and M. C. M. van Loosdrecht. 2007. Multi-scale individual-based model of microbial and bioconversion dynamics in aerobic granular sludge. Environ. Sci. Technol. 41: 6410 6417.
201. Ye, S.-Y.,, Y.-X. Qiu,, X.-L. Song,, and S.-C. Luo. 2009. Optimization of process parameters for the inactivation of Lactobacillus sporogenes in tomato paste with ultrasound and 60Co-γ irradiation using response surface methodology. Radiat. Phys. Chem. 78: 227 233.
202. Yuk, H.-G.,, and D. L. Marshall. 2003. Heat adaptation alters Escherichia coli O157:H7 membrane lipid composition and verotoxin production. Appl. Environ. Microbiol. 69: 5115 5119.
203. Zagaris, A.,, H. Kaper,, and T. Kaper. 2004. Analysis of the computational singular perturbation reduction method for chemical kinetics. J. Nonlinear Sci. 14: 59 91.
204. Zaika, L. L.,, E. Moulden,, L. Weimer,, J. G. Phillips,, and R. L. Buchanan. 1994. Model for the combined effects of temperature, initial pH, sodium chloride and sodium nitrite concentrations on anaerobic growth of Shigella flexneri. Int. J. Food Microbiol. 23: 345 358.
205. Zheng, H.,, H. Zhou,, T. Shen,, and B. Rui. 2009. Flux balance analysis within physiologically feasible region, p. 1 4. In Proceedings of the 3rd Conference on Bioinformatics and Biomedical Engineering. IEEE, Washington, DC.
206. Zobeley, J.,, D. Lebiedz,, J. Kammerer,, A. Ishmurzin,, and U. Kummer. 2005. A new time dependent complexity reduction method for biochemical systems. Trans. Comput. Syst. Biol. 3880: 90 110.
207. Zwietering, M.,, I. Jongenburger,, F. Rombouts,, and K. van ’t Riet. 1990. Modeling of the bacterial growth curve. Appl. Environ. Microbiol. 56: 1875 1881.
208. Zwietering, M. H.,, H. G. A. M. Cuppers,, J. C. de Wit,, and K. van ’t Riet. 1994. Evaluation of data transformations and validation of a model for the effect of temperature on bacterial growth. Appl. Environ. Microbiol. 60: 195 203.

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