Environmental Engineering Reference
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Fig. 3.2
Schematic representation of historical footsteps in metabolic pathways analysis. (Reproduced from http://
gcrg.ucsd.edu/sites/default/files/Attachments/Images/classes/taiwan_notes/5_slides_expa. pdf)
(1) It generates a unique and minimal set of sys-
temic pathways
(2) It describes all possible steady-state flux
distributions that the network can achieve
by non-negative linear combinations of the
extreme pathways
(3) It enables the determination of time-invari-
ant, topological properties of the network
The calculation of extreme pathways is computa-
tionally challenging and for large networks, gen-
erates a tremendous amount of numerical data
(Schilling et al.
2000
; Samatova et al.
2002
).
The phenotypic capabilities of a genome-scale
metabolic network can be characterized by a set
of systemically independent and unique extreme
pathways (Schilling et al.
2000
). Extreme path-
ways correspond to steady-state flux distribu-
tions through a metabolic network (Fig.
3.3
).
Thus, extreme pathways do not simply describe
a linear set of reactions linking substrate to
product, but instead, characterize the relative flux
Fig. 3.3
Schematic representation of a
convex cone
char-
acterized by five extreme pathways. Extreme Pathways
1-5 (
EP
1
,
EP
2
,
EP
3
,
EP
4
, and
EP
5
) circumscribe the solu-
tion space for the three fluxes indicated (
v
A
,
v
B
, and
v
C
).
EP4 lies in the plane formed by fluxes
v
A
and
v
B
. Conse-
quently, flux
v
C
does not participate in that extreme path-
way.
EP
3
, EP
4
, and
EP
5
are all close and represent differ-
ent uses of a network to achieve a similar overall result.
All points within the
convex cone
can be described as a
nonnegative linear combination of the extreme pathways.
(Reproduced from Papin et al.
2002
)
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