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updating clock)
,
k
r
(like histone acetyltransferase, endonucleases,
exonucleases, helicase, replicase, polymerases) depending on
s
microRNAs,
l
1
,
k
1
,
...
,
...
l
s
. Then the transition for a gene
i
, such as
i
does not belong to {
k
1
,
,
k
r
}, could be
...
written as:
8
{0,1}
n
,if
g
2
β2
8
j
¼
,
r
,
x
kj
(
t
)
¼
{0,1},
1,
...
1, then:
1.
P
i;g
β
ðf
x
i
ð
t
þ
1
Þ¼
gx
j
ð
t
Þ¼β
gÞ ¼
exp
½
g
ðΣ
j
2Ni
w
ij
β
j
θ
i
Þ=
T
= ½
1
þ
exp
½ðΣ
j
2Ni
w
ij
β
j
θ
i
Þ=
T
, if microRNAs
l
1
,
,
l
s
are silent
...
and
2.
P
i;0
β
ðf
x
i
ð
t
þ
1
Þ¼
0x
j
ð
t
Þ¼βg
Þ¼
1, if not.
0. To make
the transition rule more precise, we can for the sake of simplicity, decide that the
indices
k
1
,
We can remark that the case (1) implies that:
8
j
¼
1,
...
,
s
,
x
lj
(
t
-1)
¼
...
,
k
r
of the
r
“clock” genes are 1,
...
,
r
and then we have the three
possible following behaviors:
1. If
y
(
t
)
¼ Π
i¼
1,
...
,
r
x
i
(
t
)
¼
1, then the rule (2) is available
2. If
y
(
t
)
¼
0 and
Σ
s¼t
,
...
,
tc
y
(
s
)
>
0, then
x
(
t
+1)
¼
x
(
t
s*
), where
s
* is the last
time before
t
, where
y
(
s
*)
¼
1
3. If
y
(
t
)
¼
0 and
Σ
s¼t
,
...
,
tc
y
(
s
)
¼
0, then
x
(
t
+1)
¼
0 (by exhaustion of the pool
of genes still in expression)
The dynamical system remains autonomous (with respect to the time
t
, i.e.,
depends on
t
only through the set of state variables {
x
(
t
1)}), but a
theoretical study of its attractors (like in Demongeot et al.
2012
), with this state-
dependent updating schedule, is very difficult to perform and will be investigated
further by the community of biomathematicians.
c
),
,
x
(
t
...
References
Almeida L, Demongeot J (2012) Predictive power of “a minima” models in biology. Acta Biotheor
60:3-19
Aubert A, Costalat R, Magistretti PJ (2005) Brain lactate kinetics: modeling evidence for neuronal
lactate uptake upon activation. Proc Natl Acad Sci USA 102:16448-53
Aubert A, Pellerin L, Magistretti PJ, Costalat R (2007) A coherent neurobiological framework for
functional neuroimaging provided by a model integrating compartmentalized energy metabo-
lism. Proc Natl Acad Sci USA 104:4188-93
Baconnier P, Pachot P, Demongeot J (1993) An attempt to generalize the control coefficient
concept. J Biol Syst 1:335-47
Bandiera S, R¨berg S, Girard M, Cagnard N, Hanein S, Chr
´
tien D, Munnich A, Lyonnet S,
Henrion-Caude A (2011) A nuclear outsourcing of RNA interference components to human
mitochondria. PLoS ONE 6:e20746
Bandiera S, Ruberg S, Hanein S, Munnich A, Demongeot J, Lyonnet S, Henrion-Caude A (2012)
Achieving a novel dynamic in mitochondrial diseases: identification of mitochondrial
microRnas. In: Actes 6
`
mes Assises de G
´
n
´
tique Humaine et M
´
dicale. FAGHEM, Paris, p 6
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