Continuous Cultivation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 626

Mass balance of the substrate leads to

X ¼ D

m G YF X = S ðS 0 SÞ¼ 1=1000

0:000625 0:5 ð50 0:23077Þ

= ¼ 39:815 =

g L g L

which is the biomass concentration in the recycle stream.
A biomass balance around the separator yields

ð1 þ RÞQX ¼ RC R QX þ QX e

Thus,

X e ¼ð1 þ RÞX RC R X ¼ð1 þ 0:25 0:25 2:5Þ39:815 g = L ¼ 24:8846 g = L

which is the biomass concentration in the effluent stream of the chemostat system.

12.2.2. Multistage Chemostat Systems
In some fermentations, particularly for secondary metabolite production, the growth and
product formation steps need to be separated, since optimal conditions for each step are
different. Conditions such as temperature, pH, and limiting nutrients may be varied in
each stage, resulting in different cell physiology and cellular products in multistage systems.
An example of a multistage system that may be beneficial is in the culture of genetically
engineered cells. To improve genetic stability, a plasmid-carrying recombinant DNA usually
uses an inducible promoter to control production of the target protein (see Chapter 14). In the
induced state, the plasmid-containing cell grows at nearly the same rate as the cell that loses
the plasmid (a revertant), so the plasmid-free cell holds little growth advantage over the
plasmid-containing cell. However, if the inducer is added, the plasmid-containing cells
will make large quantities of the desired protein product but will have greatly reduced
growth rates. Thus, a single-stage chemostat would not be suitable for the production of
the target protein because of resulting problems in genetic stability.
A multistage system can circumvent this problem. In the first stage, no inducer is added
and the plasmid-containing cell can be maintained easily (usually an antibiotic is added to
kill plasmid-free cells; see Chapter 14 for a more complete discussion). In the second stage,
the inducer is added and large quantities of product are made. Cells defective in product
synthesis should not overtake the culture (at least not completely), because fresh genetically
unaltered cells are being continuously fed to the reactor. Thus, the two-stage system can
allow the stable continuous production of the target protein when it would be impossible
in a simple chemostat.
Perhaps an easier situation to consider is the production of a secondary product (e.g.
ethanol or an antibiotic). Here, we worry not so much about a mixture of subpopulations,
but that conditions that promote growth completely repress product formation. A very
large-scale multistage system for ethanol production is currently in use. A multistage system
of CSTR approaches PFR behavior. A PFR mimics the batch system, where space time (the
time it takes the culture fluid to reach a specific location in the PFR) replaces culture time.
A multistage system is much like taking the batch growth curve and dividing it into sections,
with each section being “frozen” in a corresponding stage of the multistage system. As in the
batch reactor, the culture's physiological state progresses from one stage to the next.