Rethinking tertiary models: Relationships between growth parameters of bacillus cereus strains

Abstract

The maximum specific growth rates of 12 strains, pair-wise belonging to six groups of Bacillus cereus sensu lato, were fitted against temperature by a reparametrized version of the model of Ratkowsky et al. (1983). This way, the interpretation of the new parameter set was similar to that of the cardinal-values-model of Rosso and Robinson (2001), both models including the minimum, optimum and maximum temperatures for growth as well as a fourth parameter scaling along the dependent variable. The modularity of the reparametrized version of the Ratkowsky model was utilized to show a so-far undetected relationship between this scaling parameter and the cardinal temperatures, which linked even distant (e.g., mesophilic and psychotropic) strains of B. cereus. We propose that the name "tertiary modeling" should be used for investigations like ours, as logically derived from the concepts of "primary" and "secondary" modeling. Such tertiary models may reveal biological relationships between kinetic parameters within a group of strains. It can also be used to create an overarching predictive model for mixed cultures, when different strains grow together but independently of each other.