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Ta b l e 3 . 2
Rule vectors of the MP grammar of Table 3.1
⎛
⎝
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
⎞
⎠
⇒
⎛
⎝
⎞
⎠
0
0
0
1
0
0
1
0
0
r
1
=
r
1
=
⎛
⎝
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
⎞
⎠
⇒
r
2
=
⎛
⎝
⎞
⎠
1
0
0
0
1
0
−
1
1
0
r
2
=
⎛
⎝
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
⎞
⎠
⇒
r
3
=
⎛
⎝
⎞
⎠
0
1
0
0
0
0
0
−
1
0
r
3
=
⎛
⎝
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
⎞
⎠
⇒
r
4
=
⎛
⎝
⎞
⎠
1
0
0
0
0
1
−
1
0
1
r
4
=
⎛
⎝
⎛
⎝
⎞
⎠
,
⎛
⎝
⎞
⎠
⎞
⎠
⇒
r
5
=
⎛
⎝
⎞
⎠
0
0
1
0
0
0
0
0
−
1
r
5
=
Ta b l e 3 . 3
The fluxes of MP rules of Table 3.1
u
1
[
i
]
:
ϕ
1
(
s
[
i
]) =
0
.
05
p
[
i
]
u
2
[
i
]
:
ϕ
2
(
s
[
i
]) =
0
.
2
C
[
i
]
u
3
[
i
]
: ϕ
3
(
s
[
i
]) =
0
.
1
u
4
[
i
]
:
ϕ
4
(
s
[
i
]) =
0
.
6
A
[
i
]
/
C
[
i
]
u
5
[
i
]
: ϕ
5
(
s
[
i
]) =
0
.
4
denotes the (column) vector of fluxes at time 0, then the
corresponding row vector of fluxes at time 0 is given by:
This means that if
U
[
0
]
(
u
1
[
0
]
,
u
2
[
0
]
,
u
3
[
0
]
,
u
4
[
0
]
,
u
5
[
0
]) = (
0
.
01
,
0
.
2
,
0
.
1
,
0
.
6
,
0
.
4
)
.
(3.6)
In this notational setting it is easy to realize that the substance variation vector
(
A
[
1
]
−
A
[
0
]
,
B
[
1
]
−
B
[
0
]
,
C
[
1
]
−
C
[
0
])
is given by the following matrix (row by column) product:
r
1
r
2
r
3
r
4
r
5
)
×
U
[
0
]=(
U
[
0
]
⎛
⎝
⎞
⎠
that is:
u
1
[
0
]
⎛
⎞
1
−
10
−
10
u
2
[
0
]
⎝
⎠
×
01
100
0001
−
u
3
[
0
]
.
−
1
u
4
[
0
]
u
5
[
0
]
