Fig. 16.6. The dependence of the specific growth rate parameter (^W) on water activity, as described by the equation of von Meien and Mitchell (2002) for two different organisms. The experimental data is from Glenn and Rogers (1988) and is reproduced with kind permission from the authors
If the kinetic model attempts to take into account the effect of both temperature and water activity on growth, the question arises as to how best to combine the effects of simultaneous variations in both variables. The best approach might be to determine the specific growth rate parameter at a large number of different combinations of water activity and temperature and simply use regression against two independent variables to determine an empirical equation (Fig. 16.7). However, to date most studies in which both water activity and temperature have been varied have not explored a sufficiently large number of combinations to allow such equations to be proposed. In the absence of this data, simple rules have been proposed for combining the effects determined in studies in which the variables are varied one-by-one, typically one variable being varied at the optimum value of the other. The maximum value of the specific growth rate constant, determined at the optimum values of water activity and temperature, is denoted noptt. During the experiments to determine the effect of each environmental variable on growth, the specific growth rate can be expressed as a fraction of this optimum:
^measured ^ opt
For example, in the case of temperature effects, using Eq. (16.13) gives:
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