Convenient Model To Describe the Combined Effects of Temperature and pH on Microbial Growth

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Abstract
A new model in which the maximum microbial specific growth rate ((mu)(infmax)) is described as a function of pH and temperature is presented. The seven parameters of this model are the three cardinal pH parameters (the pH below which no growth occurs, the pH above which no growth occurs, and the pH at which the (mu)(infmax) is optimal), the three cardinal temperature parameters (the temperature below which no growth occurs, the temperature above which no growth occurs, and the temperature at which the (mu)(infmax) is optimal), and the specific growth rate at the optimum temperature and optimum pH. The model is a combination of the cardinal temperature model with inflection and the cardinal pH model (CPM). The CPM was compared with the models of Wijtzes et al. and Zwietering et al. by using previously published data sets. The models were compared on the basis of the usual criteria (simplicity, biological significance and minimum number of parameters, applicability, quality of fit, minimum structural correlations, and ease of initial parameter estimation), and our results justified the choice of the CPM. Our combined model was constructed by using the hypothesis that the temperature and pH effects on the (mu)(infmax) are independent. An analysis of this new model with an Escherichia coli O157:H7 data set showed that there was a good correspondence between observed and calculated (mu)(infmax) values. The potential and convenience of the model are discussed.