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

Abstract

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.

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