122
Chapter 5
When it comes to the consumption of ATP in anabolic pathways the picture is much less clear.
First of all experimental studies show that copious amounts of ATP are consumed in the
biosynthetic reactions, far more than what can be calculated based on the free energy harbored in
the macromolecules which make up the cell. This is a consequence of the process where Gibbs
free energy is transferred from the catabolism to the anabolism as “discrete” packages in the form
of high-energy phosphate bonds in ATP. The ATP costs for synthesizing cell mass also varies
significantly with the environmental conditions - both due to variations in the macromolecular
composition as discussed in Section 2.1.4 and due to variations in ATP costs for maintenance of
cellular activity as will be discussed in Section 5.2.1.
In order to formalize the concept of metabolite balancing we first specify the stoichiometry for
the individual pathway reactions to be considered in the analysis. The stoichiometry for the
individual reactions is written directly into the rows of the total stoichiometric matrix
T.
The
stoichiometric coefficients for the reacting species are collected in the columns of
T.
The number
of rows in
T
is equal to
J,
the number of fluxes in the model. In the stoichiometric matrix the
compounds are organized such that the first
N
columns contain the stoichiometric coefficients for
the substrates, in the columns
N + l
to
N+M are
given the stoichiometric coefficients for the
metabolic products. Columns
N + M +l
to
N+M +K
contain the stoichiometric coefficients for the
K
intracellular metabolites. With this organization of the stoichiometric coefficients it is possible
to relate the intracellular reaction rates represented by the flux vector v to the vector r of
measurable rates given in Eq. (3.12) through:
(
r
I»,
T T\
(5.1)
In this matrix equation the last
K
rows represent the balances for the intracellular metabolites.
Example 5.1 Simple metabolic model
To illustrate the matrix equation (5.1) we consider the simple metabolic network in Fig. 5.2. From this
network the stoichiometric matrix is directly set up:
s
p,
p
2
p
3
A
B
c
r - i
0
0
0
1
0
0
0
0
0
0
- 1
1
0
0
1
0
0
0
- 1
0
0
0
0
0
0
- 1
1
0
0
1
0
0
0
- 1
, 0
0
0
1
0
0
- 1
Here the stoichiometric coefficients for the single substrate considered in the network are given in the
first column of T and the stoichiometric coefficients for the three metabolic products are given in
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