The "square-root" relationship proposed by Ratkowsky et al. (J. Bacteriol. 149:1-5, 1982) for modeling the growth rate of bacteria below the optimum growth temperature was extended to cover, the full biokinetic temperature range. Two of the four parameters of this new nonlinear regression model represent minimum and maximum temperature bounds, respectively, for the predicted growth of the

The combined effect of temperature and NaCl concentration/water activity on the growth rate of a strain of halotolerant Staphylococcus is described by the square-root models which had been used previously to model temperature dependence only. The model square root r = b(T-T min) is shown to be a special case of the Bĕlehrádek temperature function which is given by r = a(T-alpha)d. The constant alpha is the socalled 'biological zero' and equivalent to T min in the square-root models. This and the exponent d = 2 were unaffected by changing NaCl concentration/water activity. The Bĕlehrádek-type equations are preferable to the Arrhenius equation in that their parameters do not change with temperature. The constancy of T min allows derivation of a simple expression relating growth rate of strain CM21/3 to temperature and salt concentration/water activity within the range of linear response to temperature predicted by the square-root model.

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Modelling the growth response of Staphylococcus xylosus to changes in temperature and glycerol concentration/water activity. Journal of Applied Bacteriology 66, 543-548.The growth response of Staphylococcus xylosus strain CM21/3 to changes in temperature and water activity (glycerol concentration) was similar to that observed when water activity was adjusted by added NaC1. At each water activity level the effect of temperature on bacterial growth rate was described well by the square root model. TMIN (the notional minimum temperature for growth) was found to be constant and was similar to the value obtained for the same organism grown in media containing NaCI. Growth rate was proportional to glycerol concentration/water activity allowing the combined effect of this factor and temperature to be modelled by substitution of the constant b in the basic square root model by a term for water activity. The observed minimum water activity for growth at the optimum temperature was close to that predicted by the model. Several approaches to describe the growth response of micro-organisms in foods to temperature, water activity and other rate-limiting factors have been reviewed by Roberts & Jarvis (1983), Farber (1986 and Baird-Parker & Kilsby (1987). The latter indicated that two models have been used widely to measure the effect of variables on growth.The Schoolfield model (Schoolfield et al. 1981), which is a non-linear variation of the Arrhenius equation, was modified by Broughall et al. (1983) to provide a model to describe temperature and water activity effects on growth rate. Broughall & Brown (1984) extended the model to include pH as an additional factor. The square root model (Ratkowsky et al. 1982) describes growth rate with respect to temperature (Pooni