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Ta b l e 3 . 1
An MP grammar corresponding to the MP graph of Fig. 3.1
r
1
:0
→
A
ϕ
1
=
0
.
05
p
r
2
:
A
→
B
ϕ
2
=
0
.
2
C
r
3
:
B
→
0
ϕ
3
=
0
.
1
r
4
:
A
→
C
ϕ
4
=
0
.
6
A
/
C
r
5
:
C
→
0
ϕ
5
=
0
.
4
A
[
0
]=
B
[
0
]=
C
[
0
]=
1
p
[
0
]=
0
.
2,
p
[
i
+
1
]=
p
[
i
]+
0
.
2
Fig. 3.1
The MP graph corresponding to the MP grammar of Table 3.1
2. fluxes refer to the substances consumed and produced between two consecutive
steps at a fixed
time interval
with respect to which time is measured in the spe-
cific case of interest;
3. fluxes are expressed with respect a
conventional mole
, that is, a population size,
depending on the particular phenomenon in question.
Any rule
r
of an MP grammar
G
determines two column vectors: the left vector
r
−
and the right vector
r
+
. The first vector provides the multiplicity of substances
occurring in the multiset of reactants, while the second vector provides the multi-
plicities of the substances occurring in the multiset of products. The
stoichiometric
balance
r
#
r
−
(the difference of the two vectors).
The matrix consisting of the column vectors
r
+
−
of the rule
r
is defined as
r
+
−
r
−
(in a conventional order of
rules) is called the
stoichiometric matrix
of
G
. For example, the rules of MP gram-
mar of Table 3.1 could be given by Table 3.2 reporting the pair of vectors and the
corresponding stoichiometric balances.
Now, let us suppose we start from a state of a system where substances
A
C
have a 1-mole of elements (we do not enter into the specific value of our mole). Let
us denote by
A
,
B
,
[
]
,
[
]
,
[
]
the molar values of these substances at step
i
. Then, the
fluxes of our system are given, according to Table 3.1, by Table 3.3.
i
B
i
C
i
