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Applied and Environmental Microbiology, April 2007, p. 2402-2403, Vol. 73, No. 7
0099-2240/07/$08.00+0     doi:10.1128/AEM.01436-06

LETTER TO THE EDITOR

Predictions under Isothermal and Dynamically Changing Conditions


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LETTER
 
We would like to comment on a point in the paper of Fujikawa and Morozumi (2). The authors demonstrated that the model of Baranyi and Roberts (1) and their model (called model III) gave almost identical specific growth rates under isothermal conditions. Then they obtained predictions under fluctuating temperature conditions by numerically solving the respective differential equations. They found that the predictions based on the Baranyi model significantly overestimated the observed growth, while their model III worked at an acceptable accuracy in that case, too.

We point out below that this is a mathematical contradiction. Both models assume that the instantaneous slope of the growth curve is determined by the temperature at that moment, with no delay term in the equation. The model describing the effect of the temperature on the specific growth rate (secondary model) is derived from those isothermal experiments for which the Baranyi model and the authors' model III gave almost identical rates. Therefore, the two models cannot give significantly different results for dynamic situations. In Fig. 1A, the broken line represents the increase in the bacterial population as the authors produced it by means of the Baranyi model. It shows that between the sixth and the ninth hours of the experiment, the total increase is ca. 3 to 4 log10 units. This corresponds to an overall growth rate of ca. 1 to 1.3 log10 units in an hour, or a ca. 2.3- to 3-h–1 specific rate (measured on the natural-log scale). But such high specific rates were only obtained (by fitting either the authors' or the Baranyi model to log count data) at optimum temperatures, whereas in the period in question the temperature varied between ca. 20 and 25°C! Figure 1B shows similar inconsistency.


Figure 1
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  		FIG. 1. Two examples of predicted curves of Escherichia coli at dynamic temperatures. In both cases, the faster growth curves (represented by broken lines) were obtained by Fujikawa and Morozumi (2), allegedly by using the Baranyi model. The slower-growth curves (represented by thick continuous lines) were produced by us from the authors' data, also by using the Baranyi model. Circles are the experimental log counts observed by Fujikawa and Morozumi (2). The thick continuous curves are very close to the predictions obtained by the authors by using their model III.

We reproduced the authors' procedure by using their data. Our predicted curves are much slower than the authors' analogous predictions that they claim they obtained by using the Baranyi model. In fact, our curves were very close to the authors' predictions that they produced by means of their model III, similar to the isothermal situation.


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REFERENCES
 
    1
  1. Baranyi, J., and T. A. Roberts. 1994. A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23:277-294.[CrossRef][Medline]
    2. 2
  2. Fujikawa, H., and S. Morozumi. 2005. Modeling surface growth of Escherichia coli on agar plates. Appl. Environ. Microbiol. 71:7920-7926.[Abstract/Free Full Text]
Yvan Le Marc*
József Baranyi
Institute of Food Research
Norwich Research Park
Norwich NR4 7UA, United Kingdom

* Phone: 441603255021, Fax: 441603255588, E-mail: yvan.lemarc{at}bbsrc.ac.uk


Author's Reply


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LETTER 
 
For the surface growth of the test microorganism at constant temperatures, the Baranyi model and our new logistic model (model III) both made almost the same good predictions in our study (2). In contrast, the Baranyi model predicted extraordinarily fast growth under dynamic temperature conditions (2). After reading the letter to the editor by Yvan Le Marc and József Baranyi, we looked into our computer programming for solving Baranyi's differential equations (1). We found an error in the programming and corrected it. Baranyi curves prepared by using the corrected program under dynamic temperature conditions (which are being published in an author's correction) were very similar to the curves of the new logistic model. This means that both models successfully predicted bacterial growth under dynamic temperature conditions. Specifically, both models predicted almost the same growth in the exponential phase. In the acceleration and deceleration phases of growth, the Baranyi model predicted slightly higher cell densities than our model did.


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REFERENCES 
 
    1
  1. Baranyi, J., and T. A. Roberts. 1994. A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23:277-294.[CrossRef][Medline]
    2. 2
  2. Fujikawa, H., and S. Morozumi. 2005. Modeling surface growth of Escherichia coli on agar plates. Appl. Environ. Microbiol. 71:7920-7926.[Abstract/Free Full Text]
Hiroshi Fujikawa
Tokyo Metropolitan Institute of Public Health
3-24-1 Hyakunin-cho, Shinjuku
Tokyo 169-0073, Japan
Phone: 81333633231
Fax: 81333633246
E-mail: Hiroshi_1_Fujikawa@member.metro.tokyo.jp

Applied and Environmental Microbiology, April 2007, p. 2402-2403, Vol. 73, No. 7
0099-2240/07/$08.00+0     doi:10.1128/AEM.01436-06





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