Microbial growth curves: What the models tell us and what they cannot

Critical Reviews in Food Science and Nutrition

Volumn 51, Issue 10, 2011, Pages 917-945

  Micha, Peleg ^a   Corradini, Maria G ^b  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b UNIVERSIDAD ARGENTINA DE LA EMPRESA   (Argentina)

Author keywords

Gompertz model; Growth rate; Kinetics; Lag time; Logistic growth; Verhulst's equation

Indexed keywords

ADJUSTABLE PARAMETERS; ARRHENIUS MODELS; CELL DIVISIONS; CELL MORTALITY; COMBINED EFFECT; ENVIRONMENTAL FACTORS; EXTERNAL CONDITIONS; GOMPERTZ MODEL; GROWTH CURVES; GROWTH DATA; GROWTH PARAMETERS; GROWTH PATTERNS; ISOTHERMAL DATA; ISOTHERMAL GROWTH; LAG-TIME; LOGISTIC GROWTH; LOGISTIC MODELS; MATHEMATICAL DESCRIPTIONS; MATHEMATICAL SOFTWARE; MAXIMUM SPECIFIC GROWTH RATES; MECHANISTIC INTERPRETATIONS; MICROBIAL GROWTH; MICROBIAL POPULATIONS; NONISOTHERMAL; PHENOMENOLOGICAL MODELS; POPULATION DYNAMICS MODELS; PRACTICAL PROBLEMS; RATE EQUATIONS; RATE MODELS; SQUARE ROOTS; VARYING TEMPERATURE; VERHULST; WATER ACTIVITY;

CELL PROLIFERATION; CURVE FITTING; ENZYME KINETICS; GROWTH KINETICS; GROWTH RATE; PH EFFECTS; STOCHASTIC MODELS;

POPULATION STATISTICS;

BACTERIAL COUNT; BACTERIUM; BIOLOGICAL MODEL; COMPUTER PROGRAM; EMPIRICAL RESEARCH; FOOD CONTROL; GROWTH, DEVELOPMENT AND AGING; KINETICS; REVIEW; STATISTICAL MODEL;

BACTERIA; COLONY COUNT, MICROBIAL; EMPIRICAL RESEARCH; FOOD MICROBIOLOGY; KINETICS; LOGISTIC MODELS; MODELS, BIOLOGICAL; SOFTWARE;

EID: 80053320061     PISSN: 10408398     EISSN: 15497852     Source Type: Journal    
DOI: 10.1080/10408398.2011.570463     Document Type: Review

References (63)

1. Arroyo, F. N., Duran Quintana, M. C., and Fernández, A. G. (2005). Evaluation of primary models to describe the growth of Pichia anomala and study of temperature, NaCl and pH effects on its biological parameters by response surface methodology. J. Food Protect. 68: 562-570.
2. Augustin, J. C., Rosso, L., and Carlier, V. (2000). A model describing the effect of temperature history on lag time for Listeria monocytogenes. Int. J. Food Microbiol. 57: 169-181.
3. Baranyi, J., and Roberts, T. A. (1994). A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23: 277-294.
4. Baranyi, J., Robinson, T. P., Kaloti, A., and Mackey, B. M. (1995). Predicting growth of Brochothrix thermosphacta at changing temperature. Int. J. Food Microbiol. 27: 61-75.
5. Baranyi, J., and Pin, C. (1999). Estimating bacterial growth parameters by means of detection times. Appl. Environ. Microbiol. 65: 732-736.
6. Baranyi, J. and Pin, C. (2004). Modeling the history effect of microbial growth and survival: Deterministic and stochastic approaches. In McKellar, R. and Lu, X. (Eds). Modeling Microbial Response on Foods, CRC Press, FL, pp 285-301.
7. Baty, F. and Delignette-Muller, M. L. (2004). Estimating the bacterial lag time: which model, which precision? Int. J. Food Microbiol. 91: 261-277.
8. Blackburn, C. de W. (2000). Modeling shelf life. In: The Stability and Shelf Life of Food. Kilcast, D. and Subramain, P., Eds., CRC Press, Boca Raton, FL.
9. Brehm-Stecher, B. F., and Johnson, E. A. (2004). Single-cell microbiology: Tools, technologies, and applications. Microbiology and Molecular Biology Reviews 68: 538-559.
10. Brown, S. (2007). Two implications of common models of microbial growth. ANZIAM J 49 (EMAC2007): C230-C242. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/viewFile/340/239
11. Buchanan, R. L., Whiting, R. C., and Damert, W. C. (1997). When is simple good enough: A comparison of the Gompertz, Baranyi and tree-phase linear models for fitting bacterial growth curves. Food Microbiol. 14: 313-326.
12. Cornu, M., Beaufort, A., Rudelle, S., Laloux, L., Bergis, H., Miconnet, N, Serot, T., and Delignette-Muller, M. L. (2006). Effect of temperature, water-phase salt and phenolic contents on Listeria monocytogenes growth rates on cold- smoked salmon and evaluation of secondary models. Int. J. Food Microbiol. 106: 159-168.
13. Corradini, M. G., Normand, M. D., and Peleg, M. (2007). Modeling nonisothermal heat inactivation of microorganisms having biphasic isothermal survival curves. Int. J. Food Microbiol. 116: 391-399.
14. Corradini, M. G. and Peleg, M. (2005). Estimating non-isothermal bacterial growth in foods from isothermal experimental data. J. Appl. Microbiol. 99: 187-200.
15. Doona, C. J., Feeherry, F. E., and Ross, E. W. (2005). A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing. Int. J. Food Microbiol. 100: 21-32.
16. Dupont, C. and Augustin, J. C. (2009). Influence of stress on single-cell lag time and growth probability for Listeria monocytogenes in half fraser broth. Appl. Environ. Microbiol. 75: 3069-3076.
17. Elfwing, A., LeMarc, Y., Baranyi, J., and Ballagi, A. (2004). Observing growth and division of large numbers of individual bacteria by image analysis. Appl. Environ. Microbiol. 70: 675-678.
18. Fujikawa, H., Kai, A., and Morozumi, S. (2004). A new logistic model for Escherichia coli growth at constant and dynamic temperatures. Food Microbiol. 21: 501-509.
19. Fujikawa, H. and Morozumi, S. (2005). Modeling surface growth of Escherichia coli on agar plates. Appl. Environ. Microbiol. 71: 7920-7926.
20. Gibson, A. M., Baranyi, J., Pitt, J. I., Eyles, M. J., and Roberts, T. A. (1994). Predicting fungal growth: The effect of water activity on Aspergillus flavus and related species. Int. J. Food Microbiol. 23: 419-431.
21. Gospavic, R., Kreyenschmidt, J., Bruckner, S., Popov, V., and Haque, N. (2008) Mathematical modelling for predicting the growth of Pseudomonas spp. In poultry under variable temperature conditions. Int. J. Food Microbiol. 127: 290-297.
22. Guillier, L., Pardon. P., and Augustin, J. C. (2006). Automated image analysis of bacterial colony growth as a tool to study individual lag time distributions of immobilized cells. J. Microbiol. Meth., 65: 324-334.
23. Horowitz, J., Normand, M. D., Corradini, M. G., and Peleg, M. (2010). A probabilistic model of growth, division, and mortality of microbial cells. Appl. Environ. Microbiol. 76: 230-242.
24. Huang, L. (2008). Growth kinetics of Listeria monocytogenes in broth and beef frankfurters: Determination of lag phase duration and exponential growth rate under isothermal conditions. J. Food Sci. 73: E235-E242.
25. Ingraham, J. L., Maaløe, O., and Neidhart, F. C. (1983). Growth of the Bacterial Cell. Sinauer Associates, Sunderland, MA.
26. Juneja, V. K., Marks, H., and Thippareddi, H. (2009). Predictive model for growth of Clostridium perfringens during cooling of cooked ground chicken. Innov. Food Sci. Emerg. 10: 260-266.
27. Juneja, V. K., Marks, H., and Thippareddi, H. (2008). Predictive model for growth of Clostridium perfringens during cooling of cooked uncured beef. Food Microbiol. 25: 42-55.
28. Koseki, S. and Isobe, S. (2005). Prediction of pathogen growth on iceberg lettuce under real temperature history during distribution from farm to table. Int. J. Food Microbiol. 104: 239-248.
29. Koutsoumanis, K. (2001). Predictive modeling of the shelf life of fish under non-isothermal conditions. Appl. Environ. Microbiol. 67: 1821-1829.
30. Kreyenschmidt, J., Hubner, A, Beierle, E., Chonsch, L., Scherer, A., and Petersen, B. (2010). Determination of the shelf life of sliced cooked ham based on the growth of lactic acid bacteria in different steps of the chain. J. Appl. Microbiol. 108: 510-520.
31. Lambert, R. J.W. and Bidlas, E. (2007a). A study of the Gamma hypothesis: Predictive modelling of the growth and inhibition of Enterobacter sakazakii. Int. J. Food Microbiol. 115: 204-213.
32. Lambert, R. J.W. and Bidlas, E. (2007b). An investigation of the Gamma hypothesis: A predictive modelling study of the effect of combined inhibitors (salt, pH and weak acids) on the growth of Aeromonas hydrophila. Int. J. Food Microbiol. 115: 12-28.
33. Li, Y. Q., Odumeru, J. A., Griffiths, M., and McKellar, R. C. (2006). Effect of environmental stresses on the mean and distribution of individual cell lag times of Escherichia coli O157: H7. Int. J. Food Microbiol. 110: 278-285.
34. López, S., Prieto, M., Dijkstra, J., and Dhanoa, M. S. (2004). Statistical evaluation of mathematical models for microbial growth. Int. J. Food Microbiol. 96: 289-300.
35. Luera Peña, W. E., and Rodriguez de Massaguer, P. (2006). Microbial modeling of Alicyclobacillus acidoterrestris CRA 7152 growth in orange juice with nisin added. J. Food Protect. 69: 1904-1912.
36. Mataragas, M., Drosinos, E. H., Vaidanis, A., and Metaxopoulos, I. (2006). Development of a predictive model for spoilage of cooked cured meat products and its validation under constant and dynamic temperature storage conditions. J. Food Sci. 71: M1576-M167.
37. McKellar, R. and X. Lu. (Eds.) (2004). Modeling Microbial Responses on Foods. CRC Press, Boca Raton, FL.
38. McMeekin, T. A., Olley, J. N., Ross, T., and Ratkowsky, D. A. (1993). Predictive Microbiology: Theory and Application. John Wiley & Sons, New York.
39. Niven, G. W., Fuks, T., Morton, J. S., Rua, S. A.C.G., and Mackey, B. M. (2006). A novel method for measuring lag times in division of individual bacterial cells using image analysis. J. Microbiol. Meth. 65: 311-317.
40. Oscar, T. P. (2005). Development and validation of primary, secondary, and tertiary models for growth of Salmonella typhimurium on sterile chicken. J. Food Protect. 68: 2606-2613.
41. Peleg, M., Corradini, M. G., and Normand, M. D. (2009). Isothermal and non isothermal kinetic models of chemical processes in foods governed by competing mechanisms. J. Agric. Food Chem. 57: 7377-7386.
42. Peleg, M., Corradini, M. G., and Normand, M. D. (2007). The logistic (Verhulst) model for sigmoid microbial growth curves revisited. Food Res. Int. 40: 808-818.
43. Peleg, M. (2006). Advanced Quantitative Microbiology for Food and Biosystems: Models for Predicting Growth and Inactivation. CRC Press, Boca Raton, FL.
44. Peleg, M. (1997). Modeling microbial populations with the original and modified versions of the continuous and discrete logistic equations. Crit. Rev. Food Sci. 37: 471-490.
45. Pin, C. and Baranyi, J. (2008). Single-cell and population lag times as a function of cell age. Appl. Environ. Microbiol. 74: 2534-2536.
46. Pin, C. and Baranyi, J. (2006). Kinetics of single cells: Observation and modeling of a stochastic process. Appl. Environ. Microbiol. 72: 2163-2169.
47. Ratkowsky, D. A., Olley, J., McMeekin, T. A., and Ball, A. (1982). A relation between temperature and growth rate of bacterial cultures. J. Bacteriol. 149: 1-5.
48. Ratkowsky, D. A., Lowry, R. K., McMeekin, T. A., Stokes, A. N., and Chandler, R. E. (1983). Model for bacterial growth rate throughout the entire biokinetic temperature range. J. Bacteriol. 154: 1222-1226.
49. Ratkowsky, D. A. (2004a). Model fitting and uncertainty, In McKellar, R., and Lui, X. (Eds). Modeling Microbial Response on Foods. CRC Press, Boca Raton, FL, pp. 285-301.
50. Ratkowsky, D. A. (2004b). Some examples of, and some problems with, the use of nonlinear logistic regression in predictive food microbiology. Int. J. Food Microbiol. 73: 119-125.
51. Ross, E. W., Taub, I. A., Doona, C. J., Feeherry, F. E., and Kustin, K. (2005). The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods. Int. J. Food Microbiol. 99: 157-171.
52. Ross, T. and Dalgaard, P. (2004). Secondary Models in Modeling Microbial Responses in Food. pp. 63-150. McKellar, R. C. and Lu, X., Eds., CRC Press, Boca Raton, FL.
53. Ross, T. (1999). Assessment of a theoretical model for the effects of temperature on bacterial growth rate. Refrig. Sci. Technol. Proc. EUR 18816: 64-71.
54. Ross, T. (1993). Belehradek-type models. J. Ind. Microbiol. 12: 180-189.
55. Sautour, M., Dantigny, P., Divies, C., and Bensoussan, M. (2001). A temperature-type model for describing the relationship between fungal growth and water activity. Int. J. Food Microbiol. 67: 63-69.
56. Smith-Simpson, S., Corradini, M. G., Normand, M. D., Peleg, M., and Schaffner, D. W. (2007). Estimating microbial growth parameters from non-isothermal data: A case study with Clostridium perfringens. Int. J. Food Microbiol. 118: 294-303.
57. Taub, I. A., Feeherry, F. E., Ross, E. W., Kustin, K., and Doona, C. J. (2003). A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68: 2530-2537.
58. Tsoularis, A. and Wallace, J. (2002). Analysis of logistic growth models. Math. Biosci. 179: 21-55.
59. Tyrer, H., Ainsworth, P., Ibanoglu, S., and Bozkurt, H. (2004). Modelling the growth of Pseudomonas fluorescens and Candida sake in ready-to-eat meals. J. Food Eng. 65: 137-143.
60. van Boekel, M. A.J.S. (2009). Kinetic Modeling of Reactions in Foods. (Food Science and Technology). CRC Press, Boca Raton, FL.
61. Xanthiakos, K., Simos, D., Angelidis, A. S., Nychas, G. J., and Koutsoumanis, K. (2006). Dynamic modeling of Listeria monocytogenes growth in pasteurized milk. J. Appl. Microbiol. 62: 1289-1298.
62. Zwietering, M. H., Jongenburger, I., Rombouts, F. M., and van't Riet, K. (1990). Modeling of the bacterial growth curve. Appl. Environ. Microbiol. 56: 1875-1881.
63. Zwietering, M. H., Wijtzes, T., De Wit, J. C., and van't Riet, K. (1992). A decision support system for prediction of microbial spoilage in foods. J. Food Protect. 55: 973-979.