Influence of the modelling approach on the estimation of the minimum temperature for growth in Belehradek-type models

This paper compares three different approaches for describing the growth rate dependence on sub-optimal temperatures {eg, the square-roof model described by Ratkowsky et al (1982. J. Bacteriol. 154, 1222-1226):root mu =b.(T - T-min1) or mu =b(2).(T - T-min1)(2), the model originally found by Belehradek (1926a. Nature 118, 117-118): mu = a.(T - T-0)(alpha) and a dimensionless analysis described previously (Dantigny 1998. J. Ind. Microbiol. Biotechnol. 21, 215-218.): mu (dim) = [mu/mu (opt)] = [T - T-min/T-opt - T-min](alpha) = [T-dim](alpha)}. 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. T-dim and mu (dim)) or natural variables (e.g. T and mu) on the estimation of the minimum temperature for growth (e.g T-0 and T-min) and the alpha value Secondly, the Belehradek model is compared to the square-roof 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 alpha -value is significantly less than 2. In such a case, if has been highlighted that the dimensionless approach provides a closer estimation of the experimental minimum temperature for growth than the square-root model (C) 2000 Academic Press.