Biomedical Engineering Reference
In-Depth Information
Fig. 1 Fluxome solution
space of a metabolic network
in steady state obeying the
material balances of Eq. (
2
).
The solution space has the
shape of a polyhedral cone
whose edges are the
elementary modes
A
EM
¼
A
0
EM
:
ð
6
Þ
The dimension of A
EM
is m
0
9 K, where m
0
is the number of extracellular
metabolites. Each column of A
EM
contains the stoichiometry of extracellular
metabolites for the particular elementary mode. This matrix holds critical infor-
mation for process control, since it defines the theoretical metabolic footprint of
each elementary biochemical state of the cell. The specific reaction rates of
extracellular compounds are given by
b
¼
A
EM
k
:
ð
7
Þ
As shown later, these rates can be used to formulate macroscopic dynamic
models of extracellular compounds.
2.4 Example: Elementary Modes of P. pastoris
To illustrate the elementary mode concept, we have built a P. pastoris metabolic
network based on the KEGG database and papers by Chung et al. [
24
] and Çelik et al.
[
30
]. The genes associated with each reaction are in most cases known and can be
found in [
24
]. The network included the following processes/pathways: uptake
reactions (glycerol, sulfate, phosphate, and ammonia), glycolysis/gluconeogenesis,
pentose phosphate pathway, tricarboxylic acid cycle (TCA), biosynthesis of amino
acids, biosynthesis of macromolecular components of biomass (nucleotides, lipids,
carbohydrates, and proteins), and biosynthesis of a single-chain variable fragment
(scFv), interconversion of folate compounds, oxidative phosphorylation, and energy
interconversions. The metabolic network was further simplified by lumping together
in single reactions the consecutive reactions in the pathways for synthesis and
degradation of biomass and product precursors . The stoichiometry of ATP, nico-
tinamide
adenine
dinucleotide
(NADH
2
),
nicotinamide
adenine
dinucleotide
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