for temperature T in °C. The parameters ao to a4 are simply fitting parameters.

Fig. 16.3. The dependence of the specific growth rate parameter (pT) on temperature, as described by two different equations. (a) The "double-Arrhenius" equation of Saucedo-Castaneda et al. (1990). Their values for the parameters of the equation were used to plot the curve, being A = 2.694 x 1011 h-1, B = 1.3x1047, Ea1 = 70225 J mol-1, Ea2 = 283356 J mol-1. Adapted from Saucedo-Castaneda et al. (1990) with kind permission from John Wiley & Sons, Inc. (b) The general shape of the profile described by the equation set of Sangsurasak and Mitchell (1998). The parameter b allows the model to describe greater or lesser sensitivities of /uT to increases in temperature above the optimum

Fig. 16.3. The dependence of the specific growth rate parameter (pT) on temperature, as described by two different equations. (a) The "double-Arrhenius" equation of Saucedo-Castaneda et al. (1990). Their values for the parameters of the equation were used to plot the curve, being A = 2.694 x 1011 h-1, B = 1.3x1047, Ea1 = 70225 J mol-1, Ea2 = 283356 J mol-1. Adapted from Saucedo-Castaneda et al. (1990) with kind permission from John Wiley & Sons, Inc. (b) The general shape of the profile described by the equation set of Sangsurasak and Mitchell (1998). The parameter b allows the model to describe greater or lesser sensitivities of /uT to increases in temperature above the optimum

The advantage of modeling the effect of temperature is not as obvious for Cm as it is for nT. In Eq. (16.14) the maximum biomass concentration depends only on the actual temperature. Therefore Cm varies throughout the fermentation and, if the temperature falls back to the value that gives the maximum value for Cm, then the biomass is predicted to reach this value, regardless of the previous high temperatures that the culture may have suffered. In this manner, the effect of Eq. (16.14) (in combination with the kinetic equation) is simply to modify the instantaneous growth rate, not the maximum biomass concentration obtained.

It is highly likely that the temperature history affects the value of Cm. However, there is simply not sufficient data available in the literature to enable an equation to be proposed to describe this effect. One possibility might be to use Eq. (16.14), but only to allow decreases in Cm as the temperature varies above the optimum temperature. That is, once the temperature begins to fall from the maximum temperature reached during the fermentation, the value of Cm then remains fixed at the value it had at the time when the maximum temperature was reached. Experimental validation will be necessary to confirm whether this approach is appropriate.

Sangsurasak and Mitchell (1998) developed a set of empirical equations, which, although being more cumbersome than the equation used by Saucedo-Castaneda et al. (1990), does describe minimum and maximum temperatures for growth. Below the minimum temperature for growth (Tmin, °C) and above the maximum temperature for growth (Tmax, °C) the specific growth rate parameter was set to zero. Between the minimum temperature and the optimum temperature (Topt, °C) the following equation was used:

where F¡, F2, and F3 are simply fitting constants, determined by non-linear regression of the appropriate part of the curve. Between the optimum and the maximum temperature the following equation was used:

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