Biochemical Reaction Networks
125
column in the total stoichiometric matrix T that contains all the stoichiometric coefficients for ATP.
In analogy to the tight balancing of synthesis and consumption of ATP the cell needs to balance
the synthesis and consumption of the co-factors NADH or NADPH, which as mentioned in
Section 2.1.4 also have a small turnover time. Consequently the cell must exercise a strict control
of the level of these compounds as well, and balances similar to Eq. (5.2) can be set up for these
co-factors:
T r
y = 0
l NADH
v
u
(5.3)
T r
v = 0
x NADPH
V
u
(5.4)
The balances for ATP, NADH and NADPH in Eqs. (5.2)-(5.4) may be used to relate the fluxes
through different parts of the metabolic network, and as we will see in Sections 5.2.2 and 5.2.3 this
can be used to derive simple linear rate equations. However, in order to apply the ATP balance it is
important that all ATP forming and consuming reactions are considered, and we therefore first
consider an important group of energy-consuming processes inside the cell - namely
maintenance
processes.
5.2.1 Consumption of ATP for Cellular Maintenance
In 1959 it was shown by Herbert that it is necessary to consider what he called "endogenous
metabolism" when the substrate utilization for biomass growth is to be calculated. He assumed that
this endogenous metabolism results in a decrease of the amount of biomass, and he described the
degradation as a first-order process with a specific rate of biomass degradation Pe. Restitution of the
degraded biomass requires substrate, and the total substrate consumption is therefore:
( -r ) = Y ,n“ u + Y'n,e u
=
Y"“e u
+
m
V
S '
XS
/
XS
e
XS
!
s
(5.5)
Equation (5.5) shows that there are two contributions to the substrate utilization: one term which is
proportional to the observed, net specific growth rate (i.e., a growth-associated part) and another
term which counteracts the continuous degradation of the cell mass due to endogenous metabolism.
The so-called true yield coefficient specifies the yield in the conversion of substrate into biomass.
In 1965 Pirt introduced an empirical correlation identical in form to Eq. (5.5), but he collected the
product of
Y f e
and Pe in the empirical constant ms, as shown in the last expression in Eq. (5.5).
The empirical constant was called the
maintenance coefficient.
In Section 7.3.2 we are going to discuss the application of Eq. (5.5) for description of cellular
processes and show that despite its empirical nature it gives a good description of the specific
substrate uptake rate for many cellular systems. However, the simple linear rate equation does not
in a biologically satisfactory way explain what the extra substrate consumed for maintenance is in
fact used for, i.e., which energy-requiring processes inside the cell do not lead to net formation of
biomass. It is not at all clear which cellular processes should be categorized as maintenance
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