How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 576

11.7. PRODUCT YIELD

In general, microbes take nutrients from the environment to maintain the overall health of
their species (or to maintain a healthy population). One way or the other, extracellular prod-
ucts produced are related to the endogenous metabolism and/or the cell growth. The prod-
ucts are produced not because the nutrients are there and the microbes have nothing to do.
Therefore, the specific rate of microbial products formation can be written as

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

where YF P/XG is the product yield on biomass growth and YF P/e is the product yield on
endogenous needs. This is the general form of microbial product rate as related to the growth
and maintenance rates. Equation (11.38) is valid in general as the specific growth can be zero
(due to the lack of one or more growth required nutrients), but the specific product rate may
not be. Therefore, the extracellular product generation needs not be associated with the cell
growth.
Equation (11.38) can be reduced into different forms when different growth and mainte-
nance conditions are considered. When cell growth is not zero and the limiting substrate
to cell growth is also the limiting substrate for the extracellular product generation, three
simple forms of product formation rates have been shown in the literature:

1. Growth-associated products are produced simultaneously with microbial growth.
The specific rate of product formation is proportional to the specific rate of
growth, m G .

r P
X ¼

m P ¼ YF P = X m G (11.39)

The production of a constitutive enzyme is an example of a growth-associated product. It
is obtained from Eqn (11.38) when YF P/e ¼ 0 or the endogenous metabolism can be

neglected. This case is applicable in the slow growth phase.
2. Nongrowth-associated product formation takes place during the stationary phase when
the growth rate is zero due to the lack of at least one necessary substrate for growth. This
case also occurs in the fast growth regime where endogenous metabolism has reached
maximum rate. The specific rate of product formation is constant.

m P ¼ b ¼ constant (11.40)

Many secondary metabolites, such as antibiotics (for example, penicillin) production at
high cell growth rate phase and during stationary phase, are nongrowth-associated prod-
ucts. Equation (11.40) is obtained from Eqn (11.38) when m G ¼

0.

3. Luedeking e Piret equation. This is the case when K m ¼ 0when Eqn (11.38) is applied. It is often

the approximated equation based on part of the experimental data during the slow growth
and stationary phases. In this case, the specific rate of product formation is given by the:

m P ¼ b þ am G (11.41)