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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
 
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