How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 557

The reason for termination of growth may be either exhaustion of an essential nutrient or
accumulation of toxic products. If an inhibitory product is produced and accumulates in the
medium, the growth rate will slow down, depending on inhibitor production, and at a certain
level of inhibitor concentration, growth will stop. Ethanol production by yeast is an example
of a fermentation in which the product is inhibitory to growth. Dilution of toxified medium,
addition of an unmetabolizable chemical compound complexing with the toxin, or simulta-
neous removal of the toxin would alleviate the adverse effects of the toxin and yield further
growth.
The death phase (or decline phase) follows the stationary phase. However, some cell death
may start during or even before the stationary phase, and a clear demarcation between these
two phases is not always possible. Often, dead cells lyse, and intracellular nutrients released
into the medium are used by the living organisms during stationary phase. At the end of the
stationary phase, because of either nutrient depletion or toxic product accumulation, the
death phase begins. The death rate can be thought of as a first-order reaction. Because S is
zero,

m G is zero starting from the stationary phase:
r X ¼k d X (11.7)

where k d is a first-order rate constant for cell death. Mass balance of the cell biomass in the
batch reactor leads to

d ðXVÞ

dt

k d XV ¼ r X V ¼ (11.8)

which can be integrated to yield (for constant medium V):

X ¼ X S0 e k d t

(11.9)

where X S0 is the cell mass concentration at the beginning of the stationary phase.
During the death phase, cells may or may not lyse, and the reestablishment of the culture
may be possible in the early death phase if cells are transferred into a nutrient-rich medium.
In both the death and stationary phases, it is important to recognize that there is a distribution
of properties among individuals in a population. With a narrow distribution, cell death will
occur nearly simultaneously; with a broad distribution, a subfraction of the population may
survive for an extended period. It is this subfraction that would dominate the reestablish-
ment of a culture from inoculum derived from stationary- or death-phase cultures. Thus,
using an old inoculum may select for variants of the original strain having altered metabolic
capabilities.
While the phenomenological models can describe the batch experiments of cell growth
reasonably well, the parameters are not as meaningful for further genetical and more mech-
anistic evaluations. The regimes, especially the exponential phase, deceleration phase, and
stationary phase, change with different loading of the same nutrients. The cell growth is
understandably related to the availability of the substrates (or nutrients) in the medium,
which may not be due to the biomass inhibition as logistic model depicts. One can imagine
that the exponential growth is due to the sufficient supply of nutrients. The stationary phase
is due to the exhaustion of the nutrients not necessarily due to cell biomass inhibition. There-
fore, by not examining the substrate change, it leads to a noncomplete description of cell
growth.