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Table 4.7 Sequences alignment of nuclear miRNAs with adenylate/guanylate pool regulated by
genes ADK and NDK (
http://mirdborg/miRDB/
;
http://mirnamapmbcnctuedutw/
; Sbisa
et al.
1997
; Cui et al.
2007
; Bandiera et al.
2012
)
and Laurent (
1983
) for its complex kinetics], and we suppose that both pyruvate-
kinase (E4) and dehydrogenases of the complex E5 are irreversible.
Numerous
V
max
V
i
's can be diminished by the action of microRNAs inhibiting
the synthesis of the corresponding enzymes (cf. Fig.
4.12
). Let us consider now the
differential system (S1) ruling the glycolysis and the pentose pathway until the
ribulose-5-P:
V
1
x
1
n
x
1
n
V
1
x
1
n
x
1
n
d
x
1
=
d
t
¼
J
=
ð
1
þ
Þ;
d
x
2
=
d
t
¼
=
ð
1
þ
Þ
V
2
x
2
=
ð
1
þ
x
2
Þþ
L
α
V
2
x
3
=ð
1
þ
x
3
Þ;
d
x
3
=
d
t
¼ α
V
2
x
2
=ð
1
þ
x
2
Þ
V
3
x
3
=ð
1
þ
x
3
Þ
L
0
V
3
x
4
=ð
L
α
V
2
x
3
=ð
þ
x
3
Þþ
þ
x
4
Þ;
d
x
4
=
d
t
¼
V
3
x
3
=ð
þ
x
3
Þ
V
4
x
4
=
ð
þ
x
4
Þ
1
1
1
1
L
0
V
3
x
4
=ð
þ
x
4
Þ
1
x
i
1
=
2
,d
y
i
=
x
i
1
=
2
Consider now the change of variables:
y
i
¼
d
x
i
¼
=
2, where the
y
i
0
s are ruled by the differential system (S2):
=
V
1
y
1
2
n
y
1
2
n
V
1
y
1
2
n
y
1
2
n
d
y
1
=
d
t
¼
J
=
1
þ
2
y
1
;
d
y
2
=
d
t
¼½
=
1
þ
þ
=
V
2
y
2
2
y
2
2
V
2
y
3
2
y
3
2
=
1
þ
L
α
=
1
þ
2
y
2
;
ð
V
2
y
2
2
y
2
2
y
3
2
y
3
2
d
y
3
=
d
t
¼ α
=
1
þ
V
3
þ
L
α
V
2
Þ
=
1
þ
=
L
0
V
3
y
4
2
y
4
2
V
3
y
3
2
y
3
2
þ
=
1
þ
2
y
3
;
d
y
4
=
d
t
¼
=
1
þ
V
4
y
4
2
y
4
2
L
0
V
3
y
4
2
y
4
2
=
ð
1
þ
Þ
=
ð
1
þ
Þ=
2
y
4
When the attractor is a fixed point, the first enzymatic complex E1 has a stable
stationary state defined by
V
1
y
1
2
n
2
n
J
. If the steady state value
y
1
*is
reached the first among the other
y
j
*
0
s, because
V
1
is an order of magnitude higher
than the other
V
i
's, the motion of
y
1
is called rapid, and then (S2) becomes (S3):
=
ð
1
þ
y
1
Þ ¼
P
=@
P
=@
H
=@
d
y
2
=
d
t
¼@
y
2
;
d
y
3
=
d
t
¼@
y
3
þ @
y
3
;
d
y
4
=
d
t
P
=@
H
=@
¼@
y
4
þ @
y
4
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