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Ta b l e 3 . 1 8
MPF and MPR grammars providing Fibonacci's sequence
Rules
Fluxes
Reaction maps
Inertia
r
1
:
A
→
A
+
N
ϕ
1
=
A
1
=
1
ψ
A
=
0
r
2
:
N
→
A
ϕ
2
=
N
2
=
1
ψ
N
=
0
Ta b l e 3 . 1 9
An MPR system providing the dynamics given in Fig. 3.3. All inertias are 100,
the initial values are 100 for
A
,
B
,and0
.
02 for
C
.
r
1
:
A
→
2
Af
1
=
10
r
2
:
A
→
B f
2
=
0
.
02
C
r
3
:
A
→
Cf
3
=
0
.
02
B
r
4
:
B
→
0
f
4
=
4
r
5
:
C
→
0
f
5
=
4
Ta b l e 3 . 2 0
An MPR dynamically equivalent to the system given in Table 3.19 (the first
reaction of duplication becomes here an input reaction). The inertia of
A
is 110, while inertias
of
B
and
C
are 100, the initial values are 100 for
A
,
B
,and0
.
02 for
C
.
→
A
f
1
=
10
A
/
(
.
02
B
+
.
02
C
+
)
r
1
:0
0
0
110
r
2
:
A
→
B
f
2
=
0
.
02
C
r
3
:
A
→
Cf
3
=
0
.
02
B
r
4
:
B
→
0
f
4
=
4
r
5
:
C
→
0
f
5
=
4
Ta b l e 3 . 2 1
The MPF of the oscillator associated to the MPR of Table 3.20
r
1
:0
→
A
ϕ
1
=
10
A
/
(
0
.
02
B
+
0
.
02
C
+
110
)
r
2
:
A
→
B
ϕ
2
=
0
.
02
AC
/
(
0
.
02
B
+
0
.
02
C
+
110
)
r
3
:
A
→
C
ϕ
3
=
0
.
02
AB
/
(
0
.
02
B
+
0
.
02
C
+
110
)
r
4
:
B
→
0
ϕ
4
=
4
B
/
(
4
B
+
100
)
r
5
:
C
→
0
ϕ
5
=
4
C
/
(
4
C
+
100
)
3.6
Metabolic Patterns
In this section we present some basic cases of metabolic phenomena. Their com-
binations of reactions and regulations provide the majority of typical mechanisms
arising in metabolic networks, by means of
cascades
,
antagonisms
,
feedbacks
,and
delays
. The simplest mechanism of composing reactions is their sequential compo-
sition, according to which the product of a first reaction is the reactant of a second
one. A cascade is essentially given by a sequential composition of many reactions