How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 569

The balances for ATP, NADH, and NADPH are used to relate the fluxes through
different parts of the metabolic network. However, in order to apply the ATP balance, it
is important that all ATP forming and consuming reactions are considered; one group
of energy-consuming processes inside the cell, namely, maintenance processes is espe-
cially important as it is seemingly a net energy drain without an apparent benefit to the
system.
Cell maintenance is the consumption of a key substrate under consideration to maintain
the desired functionality of the cell in addition to the stoichiometrically quantifiable
desired outcome, such as cell growth. The balance of ATP, NADH, and NADPH, for
example, requires maintenance energy. Endogenous metabolism,ontheotherhand,refers
to the metabolic needs of a cell to stay viable either by consuming nutrients in the medium
when available or by converting intracellular materials when starved. Therefore, strictly
speaking, cell maintenance is cell growth dependent, while endogenous metabolic needs
are often growth independent. Cell maintenance and endogenous metabolic needs are,
however, closely related and not easily separated in practice. Therefore, these two are
often combined in bioprocess modeling, and both terminologies are used interchangeably
at times.
Herbert (D. Herbert. 1959 “Some principles of continuous culture”, Recent Prog. Microb.,
7 : 381 e 396) showed that it is necessary to consider the “endogenous metabolism” or cell
death 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
m e . Restitution of the degraded biomass requires substrate, and the total substrate consump-
tion is therefore:

r S ¼ð YF S=X m G þ YF S=X m e ÞX (11.27)

Equation (11.27) shows that there are two contributions to the substrate utilization: one term
which is directly 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 yield factor YF S/X specifies the yield in the
conversion of substrate into biomass. Pirt (S.J. Pirt. 1965 “The maintenance energy of bacteria
in growing cultures”, Proc. Royal Soc. London. Series B. 163 : 224 e 231) introduced an empirical
correlation identical in form to Eqn (11.27) , but he collected the product of YF S/X and m e in the
empirical constant m s ,

r S ¼ð YF S=X m G þ m S ÞX (11.28)

This empirical constant was called the maintenance coefficient. While strictly speaking,
maintenance requirements and endogenous needs are different, we tend to simplify the
metabolic system by “equate” the maintenance and endogenous needs. This allows us
to lump the two different indirect growth needs to one quantity. The maintenance coef-
ficient can then be related to the specific rate of substrate uptake for cellular mainte-
nance, via

m S ¼ r S j maintenance
X

¼ YF S=X k d (11.29)