Influence of the modelling approach on the estimation of the minimum temperature for growth in Belehrádek-type models Original Research Article

This paper compares three different approaches for describing the growth rate dependence on sub-optimal temperatures {e.g., the square-root model described by Ratkowsky et al. (1982. J. Bacteriol. 154, 1222–1226): √μ=b.(T−Tmin1) or μ=b2. (T−Tmin1)2, the model originally found by Belehrádek (1926a. Nature11, 117–118): μ=a. (T−T0)αand a dimensionless analysis described previously, (Dantigny 1998. J. Ind. Microbiol. Biotechnol.21, 215–218.):μdim=μμopt=T−TminTopt−Tminα=[Tdim]α}. Data sets, growth rate vs temperature, have been taken from the literature for various organisms (e.g. Lactobacillus plantarum, Yersinia enterolitica and Acinetobacter). Firstly, this paper analyses the effect of using dimensionless (e.g. Tdimand μdim) or natural variables (e.g. T and μ) on the estimation of the minimum temperature for growth (e.g. T0and Tmin) and the α value. Secondly, the Belehrádek model is compared to the square-root model by using the natural variables. It has been demonstrated that the use of the square-root model leads to an under-estimation of the minimum temperature for growth when the α -value is significantly less than 2. In such a case, it has been highlighted that the dimensionless approach provides a closer estimation of the experimental minimum temperature for growth than the square-root model.