T T

where f^optt, Tmax, and Topt were determined by visual inspection of the plot of nT against temperature, and the fitting parameter b determines the degree of curvature (Fig. 16.3(b)).

16.3.1.3 Is the "Isothermal Approach" Valid?

The dependence of the growth rate on temperature that is predicted by an equation developed using data obtained by the isothermal approach might not actually be the behavior demonstrated during an actual SSF process (Ikasari et al. 1999). There is a significant difference between the "isothermal approach" and a large-scale SSF process: the temperature in the SSF process does not remain constant; rather, it varies as a function of time. It typically begins at the optimal temperature for growth, and during the early periods the temperature is near the optimal temperature. An organism experiencing a temperature rise from the optimum to say 5°C above the optimum would very likely be healthier than an organism reaching the same temperature during the later stages of the fermentation (Fig. 16.4(a)). In the latter case the organism has recently been exposed to temperatures of as much as 10°C above the optimum, which very likely have had deleterious effects on cell structure and metabolism. The isothermal approach does not predict this, rather it assumes that the specific growth rate constant at any given instant is simply a function of the temperature at that instant (Fig. 16.4(b)).

It is highly likely that the recent history of temperatures experienced by the microorganism influences its current growth rate. For example, intracellular enzymes may denature at high temperatures, and it may take some time to replace them, meaning that high growth rates cannot immediately be re-established, even if the organism is returned to the optimum temperature. Another possibility is that senescence or sporulation may be triggered and, once triggered, may be irreversible, even if in the meantime the organism is returned to the optimal temperature. On the other hand, microorganisms do have mechanisms of adaptation to higher temperatures. Various heat shock proteins are produced and processes are induced that lead to a change in the lipid composition of the membrane. These might take several hours after an elevation of temperature to come into effect, but then growth might accelerate. Unfortunately, there is very little information available in the literature about the effect on growth kinetics of what might be called "sub-lethal temperature excursions". In the absence of more information, the best current strategy is to use the isothermal approach.

The dotted horizontal lines represent the temperature profiles experienced by the various cultures that were incubated according to the isothermal approach

Although the temperature is the same, the history of the organism is different (see the thick arrows):

• initially, the organism has been recently exposed to near-optimal temperatures

• later, the organism has been recently exposed to high temperatures

According to the curve obtained by the isothermal approach, for the same T, the value of /uj will be the same

The dotted horizontal lines represent the temperature profiles experienced by the various cultures that were incubated according to the isothermal approach

According to the curve obtained by the isothermal approach, for the same T, the value of /uj will be the same

Fig. 16.4. Is the isothermal approach valid? (a) A typical temperature profile that might occur in a large-scale bioreactor, demonstrating how the same supra-optimal temperature will be reached twice, once before the temperature peak and once after the temperature peak; (b) The isothermal approach gives the same value for /j.T, regardless of the recent temperature history of the microorganism

Recently, a model has been proposed that is capable of describing delayed temperature effects (Dalsenter et al. 2005). The model describes the effect of temperature on the relative rates of synthesis and denaturation of a pool of key metabolic enzymes (Fig. 16.5). In turn, the growth rate of the microorganism depends on the state of this enzyme pool. At the moment this model has not been sufficiently validated to have confidence that it will accurately predict growth rates under a wide range of conditions, however, it does suggest a general strategy by which future models might be developed.

16.3.2 Incorporating the Effect of Water Activity on Growth 16.3.2.1 The Experimental Approach to Collecting Data

A similar concept to the isothermal approach for determining temperature effects has been used to determine the effect of water activity on growth. Various cultures are incubated in various atmospheres of controlled relative humidity (in which the substrate is pre-equilibrated, such that its water activity is equal to the percentage

\ Auto-catalytic enzyme pool

\ Auto-catalytic enzyme pool

Specific growth rate parameter depends on the state of the enzyme pool

Fig. 16.5. Schematic representation of a model that can describe the effects of the recent temperature history on the growth rate (Dalsenter et al. 2005). F is a nondimensional variable representing the state of the intracellular "essential enzyme pool" and its value varies between 0 and 1. The coefficient of the autocatalytic synthesis reaction (kS) depends on temperature (T, °C) according to the Arrhenius equation (with frequency factor AS and activation energy EaS). The coefficient of the denaturation reaction (kD) depends on temperature according to the Arrhenius equation (with frequency factor AD and activation energy EaD)

Specific growth rate parameter depends on the state of the enzyme pool

Fig. 16.5. Schematic representation of a model that can describe the effects of the recent temperature history on the growth rate (Dalsenter et al. 2005). F is a nondimensional variable representing the state of the intracellular "essential enzyme pool" and its value varies between 0 and 1. The coefficient of the autocatalytic synthesis reaction (kS) depends on temperature (T, °C) according to the Arrhenius equation (with frequency factor AS and activation energy EaS). The coefficient of the denaturation reaction (kD) depends on temperature according to the Arrhenius equation (with frequency factor AD and activation energy EaD)

relative humidity divided by 100). The growth profile for each culture is analyzed to determine the parameters of the kinetic equation. These parameters are plotted against water activity (see Fig. 14.2) and an empirical equation is fitted to this plot. This approach is referred to here as the "isohydric approach".

In fact, the effect of water activity on growth rates in real SSF systems has been relatively little studied. Instead of this, many studies that involve fungi characterize the effect of water activity on the radial expansion rate of colonies. Furthermore, no effort has been made to look at the effect on growth of variations in the water activity during the growth cycle.

16.3.2.2 Equations that Have Been Developed Using this Approach

A simple empirical equation was used by von Meien and Mitchell (2002):

Mw =Mopt exp {D1als + D2 als + D3 aws + D4 ). (16.17)

where D1 to D4 are fitting parameters and aws is the water activity of the solid substrate phase. The symbol ¡uW is used to denote that the equation describes specifically the effect of water activity on the specific growth rate parameter. von Meien and Mitchell (2002) fitted this equation to data for two different fungi, presented by Glenn and Rogers (1998) (Fig. 16.6).

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