16.4.1 General Considerations in Modeling of Death Kinetics
Given the difficulty in controlling the fermentation conditions, especially the temperature, in large-scale SSF bioreactors, it is quite possible that conditions will occur that cause cells to die. Therefore it might be of interest to describe death kinetics within the kinetic sub-model of the bioreactor model. Note that this has often
not been done. In various bioreactor models the kinetics are written in terms of viable biomass only, with the growth rate reflecting the net increase in viable biomass, that is, the true growth rate minus the death rate. In other words, the equation only describes the overall outcome of growth and death, and does not segregate the biomass into live and dead biomass. Note that such an approach can lead to inaccuracies, since if there is significant death then the increase in viable biomass does not represent the overall growth activity. In this case growth-related activities such as metabolic heat generation would be underestimated.
In cases were death is taken into account explicitly, the growth equation is written in terms of the underlying true growth rate and a separate equation expresses the death rate. Note that many SSF processes involve fungi, and it is not necessarily a simple matter to measure fungal death experimentally. The difficulty can be seen by comparing the situation with that of studies of the death of unicellular organisms. In this case, the total cell number can be determined from total counts done in a Neubauer chamber, while the number of viable cells can be determined by viable counts, that is, agitating the culture well to separate the cells, then plating the culture out and counting the number of colonies that arise. In the case of fungi, it is not possible to separate out individual cells in this manner, since they are linked together in the mycelium. Death is often inferred by indirect means, such as a decrease in the specific O2 uptake rate. As a result, only relatively few attempts have been made to model fungal death kinetics in SSF. Further, no attempts have been made to validate the model predictions about the relative populations of live and dead biomass, rather the growth equations have simply been empirically adjusted to agree with observed growth curves.
Another factor needs to be considered. If the model describes the dry weight of the biomass, death will only cause this dry weight to decrease if the model describes a process of autolysis. In a model in which biomass dies and is converted into dead biomass, which then remains stable, it is not possible for the model to describe decreases in the overall biomass.
16.4.2 Approaches to Modeling Death Kinetics that Have Been Used
The simplest assumption is that death is a first order process, giving the equation:
where CXAV and CXAD are the absolute concentrations of viable and dead biomass, respectively, and kd is the specific death rate coefficient (h-1).
This term might simply be subtracted from the equation for the production of viable biomass. In the case in which growth follows logistic kinetics then the equation for total biomass production might be:
where CXAT is the absolute concentration of total biomass (i.e., both viable and dead). CXAT appears in the numerator of the term within the parentheses since it is assumed that the biomass-associated limitation of growth is due to the total biomass concentration and not simply the viable biomass concentration. This could be true for the case in which growth is limited by the availability of nutrients.
Subtracting the rate of death (Eq. (16.22)) from the overall rate of biomass production (Eq. (16.23)) gives the rate of increase of viable biomass:
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