How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 599

Since F P ¼ 2 Mg/year, we have

10 6

F P t
P ¼

2 22 : 66

V ¼

24 562 L ¼

9205 : 54 L

365 0 :

11.16. SUMMARY

The kinetics of cell growth and product generation is the combined effects of cell metab-
olism and cell duplication. Metabolic pathways, cell physiology, and duplication are all
important in the overall kinetic behavior. The complete description of the kinetic behavior
requires system-wide analysis (e.g. computational systems biology). In normal applications,
we deal with balanced (or pseudosteady state) growth or metabolism and thus simplification
can be applied. Multiple substrates are required for growth and fermentation; however, we
normally have many substrates in excess as compared with others. The simple growth and
product formation rate equations for the case limited by a single substrate are of Michaelis e
Menten form or the Monod equation:

r X
X ¼

m max S
K S þ S

m G ¼ (11.21)

which is the Monod equation of growth. Similarly, for extracellular product formation,

r P
X ¼

m P max S
K P þ S

m P ¼ (11.22)

which can also be expressed as

m P ¼ YF P= XG m G þ YF P = e m e (11.38)

In other words, the generation of extracellular product is almost always related to the endog-
enous metabolism of the cells and/or growth. Traditionally, there are three growth and
product rates well-known, namely, growth-associated product formation, nongrowth-associ-
ated product formation, and mixed growth-related product formation. These three cases are
all results of piece-wise interpretation (i.e. only in narrow range of growth rates) of the
growth and product formation.
Simplification or utilization of simple growth and product formation kinetic models is
valid for balanced growth (or pseudosteady state). However, there is an apparent time lag
between substrate consumption and product formation due to the inability of the simple
model to capture the uptake of substrate in the cell and a “delay” in execration of products.
This “delay” can be significant resulting in the product emerging in the fermentation broth
long after substrate had been consumed due to a “long route” of metabolic pathway.
The extracellular product generation needs not be directly associated with growth since
the growth can be limited or diminished by the lack of one or more growth required nutri-
ents. Cells can still be active other than replication. The endogenous metabolic rate also
follows the Monod rate law

r e
X ¼

m e max S
K Se þ S

m e ¼ (11.34)