Biology Reference
In-Depth Information
se
completing
P
∗
to form a cycle.
Fig. 5. The subnet
P
this end, we connect appropriate substances of
P
∗
(as fusion places) with
s
1 and/or
s
2. At this stage, one
of the advantages of the stepwise construction of the T-vector
τ
becomes clear. The tables
Consumed
Substances
resp.
Produced Substances
, derived above, exactly inform about those substances and their
amounts that have to be provided by
s
1 resp. removed by
s
2 to arrive at a (parameterized) T-invariant.
Combining this subnet
P
se
with
P
∗
by means of the fusion places, yields the cyclic net model that we
aimed at. Let denote the T-vector achieved by adding the elements
(
s
1, [ (1, ( )) ]) and (
s
2, [ (1, ( )) ]) to
τ
. Then, this T-vector has no effect and hence is a parameterized
T-invariant.
The minimal T-invariants derived by setting one of the parameters
gly
,
hex
,or
rev
to 1 (and the
remaining two to 0) are, in a short-hand notation,
τ
G
=
[(
l
1, C), (
l
2, D), (
l
3, C), (
l
4, D), (
l
5, D), (
l
7, 2
·
D), (
l
8, 2
·
D), (
s
1, D), (
s
2, D) ],
τ
P
=
[(
l
1,G+2
·
H), (
l
3, 2
·
H), (
l
4, 2
·
H), (
l
5, 2
·
H), (
l
7, 5
·
H), (
l
8, 5
·
H),
(
m
1,G+2
·
H), (
m
2, 6
·
D), (
m
3, 6
·
D),
(
r
1, G), (
r
2, 2
·
H), (
r
3, (G,H)), (
r
4, (G,H)), (
r
5, H), (
s
1, D), (
s
2, D) ],
τ
R
=
[(
l
1, G
), (
l
2
,2
·
H
), (
l
7, H
), (
l
8, H
), (
m
1, G
+2
·
H
), (
m
2, 6
·
D), (
m
3, 6
·
D),
(
r
1, G
), (
r
2, 2
·
H
), (
r
3, (G
,H
)), (
r
4, (G
,H
)), (
r
5, H
), (
s
1, D), (
s
2, D) ].
The three T-invariants
τ
G
,
τ
P
,
τ
R
are linearly independent and hence form a basis.
