e controlled air flow rate with known %O2
O2 analyzer multiple chambers, one sacrificed at each time to determine biomass calculation of O2 uptake rate (OUR, mol h-1) from A[O2] and flow rate (Eq. (17.6))
integrate resulting equation (e.g., with logistic equation will arrive at Eq. (17.7))
fit equation (e.g. Eq. (17.7)) to experimental COU curve by non-linear regression to give values for Yxo and mo integrate resulting equation (e.g., with logistic equation will arrive at Eq. (17.7))
fit equation (e.g. Eq. (17.7)) to experimental COU curve by non-linear regression to give values for Yxo and mo
Fig. 17.2. Procedure by which YXO and mo can be determined experimentally during the kinetic studies. The example shows direct biomass measurement by membrane filter culture. However, the same procedure can be undertaken in fermentations of the substrate that is used in the SSF process if a component of the biomass is measured and the kinetics are expressed in terms of this component assuming a COU of 0 at zero time. This equation appears complex, but the values of Xm, Xo, and n are already known from the regression analysis of the biomass profile. The only two remaining unknowns are YOX and mo, and these can be determined by non-linear regression of Eq. (17.7) against the experimental profile for COU against time.
Similar equations could be derived for exponential and linear growth kinetics. However, this would be more complicated, because these simple equations typically only describe a part of the growth profile in a SSF process, so a "piecewise fitting" of the growth and profile might need to be made.
This analysis can also be done in a system in which biomass can only be measured indirectly, through determination of a component of the biomass. In this case X would represent the absolute amount of component and YXO and mo would express the relationships between O2 and the component.
17.2.5 General Considerations with Respect to Equations for the Effects of Growth on the Environment
Within the various bioreactor models that have been proposed to date, the maintenance term (the second term on the right-hand side of Eqs. (17.1) to (17.5)) has often been omitted. This has been done to simplify the equation and not because maintenance metabolism is negligible. In fact, due to the physiological stress that the microorganism experiences during SSF, maintenance metabolism is often significant.
The procedure outlined in Fig. 17.2 for the determination of YXO and mo can potentially be adapted to determine the yield and maintenance parameters for heat, nutrients, and CO2 (the case of water is more difficult due to the possibility of evaporation occurring). This procedure is somewhat more complicated than the determination of yield and maintenance coefficients in continuous culture in an SLF system. However, these parameters should not be determined in continuous SLF since the yield and maintenance coefficients in liquid culture will likely be quite different from those in SSF.
This procedure for determining yield and maintenance coefficients would typically be undertaken at the optimal values of temperature and water activity. However, in reality, these coefficients will be functions of temperature and water activity, and the temperature and water activity vary during the fermentation within a large-scale SSF bioreactor. A large amount of effort would be required to obtain sufficient experimental data to allow these coefficients to be expressed as functions of the environmental conditions. In the great majority of cases this has not been done, rather, these coefficients have been treated as constants, determined under controlled conditions at laboratory-scale. One exception is the work of Smits et al. (1999) where the maintenance coefficients were expressed as a function of the fermentation time. For example, their equation for O2 consumption was written as:
yxo dt where the value of D changes over time, causing the apparent maintenance coefficient to change. Note that this could represent the situation in which the true maintenance coefficient was constant but biomass was dying, such that not all of the biomass was contributing to maintenance activity. Smits et al. (1999) investigated various forms of expressions for D, noting that realistic predictions for their system were given by the following:
This model says that before td there is no death, that is, all the biomass contributes to maintenance metabolism, then between td and tr there is a linear decline in maintenance activity. After time tr there is a new and constant level of specific maintenance activity, equal to (mo-md (tr-td)). They determined the values for md, td, and tr by comparing experimental profiles for the biomass with the experimental O2 uptake rate results.
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