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time time if the predicted curve does not fit well, change the values of YXS and ms and redo the integration

Stop when a good fit is obtained after integration

Fig. 16.2. How estimates of YXS and mS can be obtained if, during the initial laboratory studies (See Chaps. 14 and 15), growth profile data is obtained in both the absolute and relative concentrations. Note that optimization programs can be used to undertake the iterative fitting of the relative biomass curve

The sections below present experimental approaches that can be used to gather experimental data, and approaches to developing appropriate equations, for the case of temperature and the case of water activity. Note that the recommendations are for "isothermal" and "isohydric" studies, in which conditions are maintained constant throughout the growth cycle, whereas in real SSF processes the temperature and the water activity change during the process. It is possible that expressions for the effects of temperature and water activity that are obtained on the basis of the isothermal and isohydric approaches will not describe the true effect on growth of the time-varying conditions that are encountered by the organism in SSF processes at large scale (Ikasari et al. 1999). The advantage of the isothermal and isohydric approaches is that they are easy to carry out. Possible approaches to determining the effects of temporal variations in the environmental variable are also discussed.

16.3.1 Incorporating the Effect of Temperature on Growth

16.3.1.1 The "Isothermal Approach"

This experimental approach is as follows (see Fig. 14.2):

1. A small-scale experimental system is used so that heat transfer will not be limiting (see Sect. 15.1) and therefore the substrate will be at the temperature of the incubator or waterbath used;

2. Cultures are incubated at various different temperatures, with the temperature experienced by each culture being held constant during the entire growth cycle;

3. The growth profile for each culture is then plotted and the appropriate kinetic equation is fitted to each profile, allowing determination of the values of the parameters of the kinetic equation for each temperature. For example, if the growth curve is logistic, the integrated form of the logistic equation is fitted by non-linear regression to the growth profile. This will yield a specific growth rate constant and a maximum biomass concentration for each temperature;

4. The parameters that are sensitive to temperature are then plotted against temperature and an empirical equation is used to describe this curve, being fitted to the curve by non-linear regression.

16.3.1.2 Equations that Have Been Developed Using this Approach

Equations that have been used to describe the effect of temperature on growth are presented below. All are simply empirical fits to the data.

Saucedo-Castaneda et al. (1990) used a "double Arrhenius" equation to describe the effect of temperature on the specific growth rate constant:

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