How Cells Grow - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 571

Here r ATP specifies the total formation rate of ATP in catabolic pathways (different from the
net formation rate of ATP, which is implicitly assumed to be zero in the equation). From
precise measurements of the metabolic products of the anaerobic metabolism, it is possible
to calculate the specific formation rate of ATP, i.e. r ATP . This may be used to find experimental
values for YF ATP/X and m ATP , as shown in many studies. In aerobic processes, a major part of
the ATP formation originates in the respiration, and the yield of ATP in this process is given
by the P/O ratio. It is difficult to estimate the operational value of the P/O ratio. Detailed
empirical studies (e.g. W.M. van Gulik, J.J. Heijnen. 1995 “Ametabolic network stoichiometry
analysis of microbial growth and product formation”, Biotechnol. Bioeng. 48 : 681 e 698) have
indicated an operational P/O ratio of 1.2 e 1.3, but this will depend on the microorganism
and perhaps also on the environmental conditions. The ATP production can therefore not
be calculated with the same accuracy in organisms that gain ATP by respiration as for organ-
isms that are only able to produce ATP in fermentative pathways (substrate-level
phosphorylation).
In Table 11.2 , experimentally determined values for YF ATP/X and m ATP are collected for
a number of microorganisms growing at anaerobic conditions where r ATP could be precisely
determined. There is a large variation in the experimentally found values. This is partly
explained by the fact that YF ATP/X depends both on the applied medium and on the macro-
molecular composition of the biomass. However, more definitive explanation that lies on the
maintenance cost can have a different rate than the cell growth.
Instead of focusing on simple empirical correlations of cell maintenance with cell growth
rate, we next examine the cell maintenance from a more mechanistic point of view. As we
have learnt that the Monod equation is an approximated growth rate from the complicated
metabolic pathways (section 11.4). The same approximation can be applied to be based on

a key intermediate (for example ATP), rather than the substrate from the environment.
Let us denote this key intermediate as Y, the specific cell growth rate can then be approxi-
mated by

x

r X m max Y

K YG þ

m G ¼

X ¼

(11.32)

Y

While Y is the intermediate for cells to add mass (grow), it is consumed to maintain the cell
active. For example, one can assume Y to be M 2 for the simple metabolic pathway in Fig. 11.3 .
The maintenance cost of the intermediate Y can be assumed to be in a fashion similar to any
other bioreactions. In other words, the maintenance (or endogenous) cost can be approxi-
mated by

r e
X ¼

m e max Y
K Ye þ

m e ¼ (11.33)

Y

where the saturation constant K Ye needs not to be identical to the saturation constant K Y in the
cell growth rate. K Ye may not be exactly zero either (for which a constant maintenance coef-
ficient prevails). There are two ways to express the cell maintenance cost, either to the cell
growth rate or to the substrate availability. It is not difficult to see that

r e

X ¼ m emax S

m e ¼ (11.34)

K Se þ S