Biology Reference
In-Depth Information
Consumed substances
ADP:
(2
·
gly
+5
·
hex
+
rev
)'D
ATP:
(2
·
gly
+5
·
hex
+
rev
)'D
2
·
rev
'H
gly
'C +
hex
'G+2
·
hex
'H +
rev
'G
F6P:
Gluc:
(3
·
hex
+3
∗
rev
)'D
GSSG:
(6
·
hex
+6
·
rev
)'D
H
2
O:
NAD
+
:
NADP
+
:
2
·
gly
+5
·
hex
+
rev
)'D
6
·
hex
+6
·
rev
)'D
P
i
:
(2
·
gly
+5
·
hex
+
rev
)'D
Produced substances
ATP:
(4
·
gly
+10
· h
ex+2
· r
ev)'D
(3
·
hex
+3
·
CO
2
:
rev
)'D
rev
'H
F6P:
2
·
GSSG:
(6
·
hex
+6
·
rev
)'D
hex
'H +
r
ev 'H
H
2
O:
(2
·
gly
+5
·
hex
+
rev
)'D
Lac:
2
·
gly
'C + 5
·
NAD
+
:
NADP
+
:
(2
·
gly
+5
·
(6
·
hex
+6
·
hex
+
re
v)'D
rev
)'D
Parameters
Overall reaction
(G)
gly
=
1
2 ADP
+
Gluc
+
2P
i
=
2ATP+2Lac+2H
2
O
(P)
hex
=
1
5 ADP
+
3 Gluc
+
5P
i
=
5ATP+5Lac+3CO
2
+2H
2
O
(R)
rev
=
1
ADP
+
Gluc
+
P
i
+
2H
2
O
=
ATP+Lac+3CO
2
(
m
2, [ (6, (
hex
+
rev
)'( )) ]),
(
m
3, [ (6, (
hex
+
rev
)'( )) ]),
(
r
1, [ (1,
hex
'(x
G)), (1,
rev
'(x
G')) ]),
(
r
2, [ (2,
hex
'(y
H)), (2,
rev
'(y
H')) ]),
(G
,H
))
) ]),
(
r
3, [ (1,
hex
'((x,y)
(G,H))), (1,
rev
'((x,y)
(G
,H
))
) ]),
(
r
4, [ (1,
hex
'((x,y)
(G,H))), (1,
rev
'((x,y)
H
))
]),
(
r
5, [ (1,
hex
'(y
H)), (1,
rev
'(y
(
l
2
, [ (2,
rev
'( )) ]) ].
The T-vector
τ
represents three vectors, one for each parameter, which correspond to the expected three
elementary modes. They are identical to those computed by S. Schuster, using METATOOL. Applying
the function EFFECT from the package SY to
τ
yields its effect, which is equal to the difference between
Produced substances
and
Consumed substances
,
ADP:
−
2
·
gly
'D
−
5
·
hex
'D -
rev
'D,
ATP: 2
·
gly
'D + 5
·
hex
'D +
rev
'D,
CO
2
:3
·
hex
'D + 3
·
rev
'D,
rev
'G
,
Gluc:
−
gly
'C -
hex
'G
−
2
·
hex
'H
−
H
2
O: 2
·
gly
'D + 2
·
hex
'D
−
2
·
rev
'D,
hex
'H +
rev
'H
,
Lac: 2
·
gly
'C + 5
·
P
i
:
−
2
·
rev
'D.
Neglecting the token colors, this leads to the parameterized equation for the effect of
τ
(2
·
gly
'D
−
5
·
hex
'D
−
gly
+5
·
hex
+
rev
)'ADP + (
gly
+3
·
hex
+
rev
)'Gluc + (2
·
gly
+5
·
hex
+
rev
)'P
i
+2
·
hex
'H
2
O=(2
·
gly
+5
·
hex
+
rev
)'ATP + (2
·
gly
+5
·
hex
+
rev
)'Lac + (3
·
hex
+3
·
rev
)'CO
2
+(2
·
gly
+2
·
hex
)'H
2
O yielding
the three
overall reaction
equations for the elementary modes.
T-invariants describe processes in a Petri net which restore the marking with which they started and
thus can be executed cyclically. Clearly,
τ
is
not
a T-invariant. Because in
P
∗
all paths containing Gluc
and Lac are not cyclic,
no
full T-vector
at all
can be a T-invariant. Therefore, we modify the model
P
∗
by glueing it with a subnet
P
se
(depicted in Fig. 5) that closes the cycle from Lac to Gluc. This subnet
contains a place StartEnd, initially marked by a dummy token D, and the transitions s1 for starting and
s2 for ending a cyclic run. The transitions
s
1 and
s
2 are intended to compensate the non-null effects. To
