Utility of phenomenological models for describing temperature dependence of bacterial growth

We compared three unstructured mathematical models, the master reaction, the square root, and the damage/repair models, for describing the relationship between temperature and the specific growth rates of bacteria. The models were evaluated on the basis of several criteria: applicability, ease of use, simple interpretation of model parameters, problem-free determination of model parameters, statistical evaluation of goodness of fit (chi 2 test), and biological relevance. Best-fit parameters for the master reaction model could be obtained by using two consecutive nonlinear least-square fits. The damage/repair model proved to be unsuited for the data sets considered and was judged markedly overparameterized. The square root model allowed nonproblematical parameter estimation by a nonlinear least-square procedure and, together with the master reaction model, was able to describe the temperature dependence of the specific growth rates of Klebsiella pneumoniae NCIB 418, Escherichia coli NC3, Bacillus sp. strain NCIB 12522, and the thermotolerant coccobacillus strain NA17. The square root and master reaction models were judged to be equally valid and superior to the damage/repair model, even though the square root model is devoid of a conceptual basis.