Biochemical Reactions - A First Look
53
medium.
From measurements of the concentrations of the variables at a fixed value of the input variable
D
the reaction rates can easily be determined from the mass balances (3.2)-(3.4) or (3.5)-(3.10) if there
is an exchange with a gas phase.
In an experiment used to determine the reaction rates a number of the variables in the mass balances
are usually zero.
Typically there is neither biomass nor product in the feed streams, i.e.,
Xf=P'j=*<r
=0
(3-11)
Components transferred from the gas phase are typically only sparingly soluble. In
particular this is true for oxygen and also for natural gas, the carbon and energy source used
in modem single cell protein production. Typically
= XmM
and
so2
=
10-20
/jM
while the corresponding values for
sCH
are a little lower for SCP production. Thus in (3.7)
and (3.10)
Si
can be set to zero. In other aerobic bioreactions
sQ
has to be a sizeable
fraction of
So2
-
perhaps 10% for penicillin fermentation and even 25-35% for baker’s yeast
production.
In equations (3.2) to (3.4)
q,
is the volumetric production rate, i.e., the mass of compound
i
produced per volume reactor and per unit time. The rates of the bioreactions, i.e., of the reactions
within the cell, conventionally measured in mass of the ith component produced per unit weight of
cell (rather than per unit volume of cell) and per unit time are:
r(
<7,
X
(3.12)
and specifically for the biomass:
H = i\
q
= the specific growth rate
(3.13)
As mentioned in Section 1.2
r,
are the rates associated with the “real” reactions in the “real” reactor
- the cell, whereas
q,
is used in mass balances set up for the reactor vessel.
3.2
Yield Coefficients
When any particular rate, whether
q,
or
r,
is scaled with another rate
qs
or r, one obtains the
yield
coefficient Y)y