Development of Predictive Mathematical Model for the Growth Kinetics of Staphylococcus aureus by Response Surface Model

  • Seo, Kyo-Young (Department of Food Science and Technology, Chung-Ang University) ;
  • Heo, Sun-Kyung (Department of Food Science and Technology, Chung-Ang University) ;
  • Lee, Chan (Department of Food Science and Technology, Chung-Ang University) ;
  • Chung, Duck-Hwa (Division of Applied Life Science, Gyeongsang National University) ;
  • Kim, Min-Gon (Laboratory of Integrative Biotechnology, Korea Research Institute of Bioscience and Biotechnology) ;
  • Lee, Kyu-Ho (Department of Environmental Engineering and Biotechnology, Hankuk University of Foreign Studies) ;
  • Kim, Keun-Sung (Department of Food Science and Technology, Chung-Ang University) ;
  • Bahk, Gyung-Jin (Korea Health Industry Development Institute) ;
  • Bae, Dong-Ho (Division of Bioscience and Biotechnology, Konkuk University) ;
  • Kim, Kwang-Yup (Department of Food Science and Technology, Chungbuk University) ;
  • Kim, Cheorl-Ho (Department of Biological Sciences, College of Natural Science, Sungkyunkwan University) ;
  • Ha, Sang-Do (Department of Food Science and Technology, Chung-Ang University)
  • Published : 2007.09.30


A response surface model was developed for predicting the growth rates of Staphylococcus aureus in tryptic soy broth (TSB) medium as a function of combined effects of temperature, pH, and NaCl. The TSB containing six different concentrations of NaCl (0, 2, 4, 6, 8, and 10%) was adjusted to an initial of six different pH levels (pH 4, 5, 6, 7, 8, 9, and 10) and incubated at 10, 20, 30, and $40^{\circ}C$. In all experimental variables, the primary growth curves were well ($r^2=0.9000$ to 0.9975) fitted to a Gompertz equation to obtain growth rates. The secondary response surface model for natural logarithm transformations of growth rates as a function of combined effects of temperature, pH, and NaCl was obtained by SAS's general linear analysis. The predicted growth rates of the S. aureus were generally decreased by basic (pH 9-10) or acidic (pH 5-6) conditions and higher NaCl concentrations. The response surface model was identified as an appropriate secondary model for growth rates on the basis of correlation coefficient (r=0.9703), determination coefficient ($r^2=0.9415$), mean square error (MSE=0.0185), bias factor ($B_f=1.0216$), and accuracy factor ($A_f=1.2583$). Therefore, the developed secondary model proved reliable for predictions of the combined effect of temperature, NaCl, and pH on growth rates for S. aureus in TSB medium.


  1. Adair, C., D. C. Kilsby, and P. T. Whittall. 1989. Comparison of the School field (non-linear Arrhenius) model and the square root model for predicting bacterial growth in foods. Food Microbiol. 6: 7-18
  2. Bean, N. H. and P. M. Griffin. 1990. Foodborne disease outbreaks in the United States, 1973-1987: Pathogens, vehicles and trends. J. Food Prot. 53: 804-817
  3. Bergdoll, M. S. 1989. Staphylococcus aureus, pp. 463-513. In M. P. Doyle (ed.), Foodborne Bacterial Pathogens. Marcel Dekker, Inc., New York
  4. Bergdoll, M. S. 1992. Staphylococcal intoxication in mass feeding, pp. 25-47. In A. T. Tu (ed.), Foodpoisoning: Handbook of Natural Toxins, Vol. 7. Marcel Dekker, Inc., New York
  5. Bhaduri, S., C. O. Turner-Jones, R. L. Buchanan, and J. G. Phillips. 1994. Response surface models of the effect of pH, sodium chloride and sodium nitrite on growth of Yersinia enterocolitica at low temperatures. Int. J. Food Microbiol. 23: 333-343
  6. Bovill, R., J. Bew, N. Cook, M. D'Agostino, N. Wilkinson, and J. Baranyi. 2000. Predictions of growth for Listeria monocytogenes and Salmonella during fluctuating temperature. Int. J. Food Microbiol. 59: 157-165
  7. Buchanan, R. L. 1993. Predictive food microbiology. Trends Food Sci. Technol. 4: 6-11
  8. Buchanan, R. L., L. K. Bagi, R. V. Goins, and J. G. Phillips. 1993. Response surface model for the growth kinetics of Escherichia coli O157:H7. Food Microbiol. 10: 303-315
  9. Buchanan, R. L. and J. G.. Phillips. 1990. Response surface models for predicting the effects of temperature, pH, sodium chloride content, sodium nitrite concentration and atmosphere on the growth of Listeria monocytogenes. J. Food Prot. 53: 370-376
  10. Dalgaard, P., T. Ross, L. Kamperman, K. Neumeyer, and T. A. McMeekin. 1994. Estimation of bacterial growth rates from turbidimetric and viable count data. Int. J. Food Microbiol. 23: 391-404
  11. Dlgaard, 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
  12. Duffy, L. L., P. B. Vanderlinde, and F. H. Grau. 1994. Growth of Listeria monocytogenes on vacuum-packed cooked meats: Effects of pH, $a_w$, nitrite and ascorbate. Int. J. Food Microbiol. 23: 377-390
  13. El-Gazzar, F. E. and E H. Marth. 1975. Salmonellae, salmonellosis, and dairy foods: A review. J. Dairy Sci. 75: 2327-2343
  14. Gibson, A. M., N. Bratchell, and T. A. Roberts. 1988. Predicting microbial growth: Growth responses of Salmonella in a laboratory medium as affected by pH, sodium chloride and storage temperature. Int. J. Food Microbiol. 6: 155-178
  15. GraphPad Software Inc. 2003. User's Guide. San Diego, California, U.S.A
  16. Grau, F. H. and P. B. Vanderlinede. 1993. Aerobic growth of Listeria monocytogenes on beef lean and fatty tissue: Equations describing the effects of temperature and pH. J. Food Prot. 56: 96-101
  17. Holmberg, S. D. and P. A. Blake. 1984. Staphylococcal food poisoning in the United States. JAMA 251: 487-489
  18. ICMSF. 1996. Staphylococcus aureus, pp. 299-333. In T. A. Roberts, A. C. Baird-Parker, and R. B. Tompkin (eds.), Microorganisms in Foods 5: Characteristics of Microbial Pathogens. Blackie Academic & Professional, London
  19. Jablonski, L. M. and G. A. Bohach. 1997. Staphylococcus aureus, pp. 353-375. In M. P. Doyle, L. R., Beuchat, and T. J. Montville (eds.), Food Microbiology: Fundamentals and Grontiers. ASM Press, Washington, D. C
  20. Jung, H. J., K. S. Choi, and D. G. Lee. 2005. Synergistic killing effect of synthetic peptide P20 and cefotaxime on methicillin-resistant nosocomial isolate of Staphylococcus aureus. J. Microbiol. Biotechnol. 15: 1039-1046
  21. Ko, K. S., J. Y. Lee, J. H. Song, J. Y. Baek, W. S. Oh, J. S. Chun, and H. S. Yoon. 2006. Screening of essential genes in Staphylococcus aureus N315 using comparative genomics and allelic replacement mutagenesis. J. Microbiol. Biotechnol. 16: 623-632
  22. Lee, H. W., J. H. Yoon, J. H. Sohn, K. H, Lee, B. I. Yeh, D. W. Park, H. W. Kim, and J. W. Choi. 2003. Detection of MecA gene in clinical isolates of Staphylococcus aureus by multiple-PCR, and antimicrobial susceptibility of MRSA. J. Microbiol. Biotechnol. 13: 354-359
  23. McClure, P. J., C. D. Blackburn, M. B. Cole, P. S. Curtis, J. E. Jones, J. D. Legan, I. D. Ogden, M. W. Peck, T. A. Roberts, J. P. Sutherland, and S. J. Walker. 1994. Modelling the growth, survival and death of microorganisms in foods: The UK Food Micromodel approach. Int. J. Food Microbiol. 23: 265-275
  24. Mead, P. S., L. Slutsker, V. Dietz, L. F. McCraig, J. S. Bresee, C. Shapiro, P. M. Griffin, and R. V. Tauxe. 1999. Food-related illness and death in the United States. Emerg. Infect. Dis. 5: 607-625
  25. Nerbrink, E., E. Borch, H. Blom, and T. Nesbakken. 1999. A model based on absorbance data on the growth rate of Listeria monocytogenes and including the effects of pH, NaCl, Na-lactate and Na-acetate. Int. J. Food Microbiol. 47: 99-109
  26. Neumeyer, K., T. Ross, and T. A. McMeekin. 1997. Development of a predictive model to describe the effects of temperature and water activity on the growth of spoilage Pseudomonas. Int. J. Food Microbiol. 38: 45-54
  27. Oscar, T. P. 1999. Response surface models for effects of temperature and previous growth sodium chloride on growth kinetics of Staphylococcus aureus on cooked chicken breast. J. Food Prot. 62: 1470-1474
  28. Oscar, T. P. 2002. Development and validation of a tertiary simulation model for predicting growth of Staphylococcus aureus on cooked chicken. Int. J. Food Microbiol. 76: 177-190
  29. Palumbo, S. A., A. C. Williams, R. L. Buchanan, and J. G. Phillips. 1991. Model for the aerobic growth of Aeromonas hydrophila K144. J. Food Prot. 54: 429-435
  30. Park, S. H., H. J. Kim, and H. Y. Kim. 2006. Simulaneous detection of Yersinia enterocolitica, Staphylococcus aureus, and Shigella spp. in lettuce using multiplex PCR method. J. Microbiol. Biotechnol. 16: 1301-1305
  31. Park, S. Y., J. W. Choi, J. H. Yeon, M. J. 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. 2005. Predictive modeling for the growth of Listeria monocytogenes as a function of temperature, NaCl, and pH. J. Microbiol. Biotechnol. 15: 1323-1329
  32. Ross, T. 1996. Indices for performance evaluation of predictive models in food microbiology. J. Appl. Bacteriol. 81: 501-508
  33. Ross, T. 1999. Predictive Food Microbiology Models in the Meat Industry. Meat and Livestock Australia, Sydney, Australia
  34. Ross, T., P. Dalgaard, and S. Tienungoon. 2000. Predictive modelling of the growth and survival of Listeria in fishery products. Int. J. Food Microbiol. 62: 231-245
  35. SAS Institute Inc. 2002. SAS User's Guide. Statistical Analysis Systems Institute, Cary, NC, U.S.A
  36. Schaffner, D. W. and T. P. Labuza. 1997. Predictive microbiology: Analyzing the present and the future. Food Technol. 51: 95-99
  37. Skinner, G. E., J. W. Larkin, and E. J. Rhodehamel. 1994. Mathematical modeling of microbial growth: A review. J. Food Safety 14: 175-217
  38. Soboleva, T. K., A. B. Pleasants, and G. le Roux. 2000. Predictive microbiology and food safety. Int. J. Food Microbiol. 57: 183-192
  39. Sutherland, J. P., A. J. Bayliss, and T. A. Roberts. 1994. Predictive modeling of growth of Staphylococcus aureus: The effects of temperature, pH, and sodium chloride. Int. J. Food Microbiol. 21: 217-236
  40. Whiting, R. C. 1995. Microbiogical modeling. Crit. Rev. Food Sci. Nutr. 35: 457-494
  41. Whiting, R. C. and R. L. Buchanan. 1997. Predictive modeling, pp. 728-739. In M. P. Doyle, L. R. Beuchat, and T. J. Montville (eds.), Food Microbiology: Fundamentals and Frontiers. ASM Press, Washington, D.C
  42. Wilson, P. D. G., D. R. Wilson, T. F. Brocklehurst, H. P. Coleman, G. Mitchell, C. R. Waspe, S. A. Jukes, and M. M. Robins. 2003. Batch growth of Staphylococcus aureus LT2: Stoichiometry and factors leading to cessation of growth. Int. J. Food Microbiol. 89: 195-203
  43. Zurera-Cosano, G., A. M. Castillejo-Rodríguez, R. M. García-Gimeno, and F. Rincón-Leon. 2004. Performance of response surface and Davey model for prediction of Staphylococcus aureus growth parameters under different experimental conditions. J. Food Prot. 67: 1138-1145