Biology Reference
In-Depth Information
Fig. 3. Continuous and discrete transitions of
hybrid functional Petri net
. (a) An example of continuous transition. Four input
arcs are attached to continuous transition
T
C
: two continuous input arcs from continuous places
P
1 and
P
4
, and two test input
arcs from continuous place
P
2
and discrete place
P
3
.
a
i
is the weight of arc from place
P
i
fori=1,2,3,4. Twocontinuous
arcs are headed from the transition
T
C
to continuous places
Q
1
and
Q
2
, respectively. Variables
b
1
and
b
2
are assigned to these
arcs as weights. (b) An example of discrete transition. Four input arcs are attached to discrete transition
T
D
: two discrete input
arcs from discrete place
P
1
and continuous place
P
3
, and two test input arcs from discrete place
P
2
and continuous place
P
4
.
a
i
is the weight of arc from place
P
i
for
i
=
1, 2, 3, 4. Two output arcs are headed from the transition
T
D
to discrete place
Q
1
and
continuous place
Q
2
. Variables
b
1
and
b
2
are assigned to these arcs as weights.
Fig. 4. The gene regulation in the
Drosophila
circadian oscillator is schematized.
(
dbt
). It is known that the
Drosophila
circadian feedback system is composed of two interlocked negative
feedback loops [10]. Roughly speaking, PER and TIM proteins collaborate in the regulation of their
own expression in
Drosophila
, assembling in PER-TIM complexes that permit nuclear translocation,
inactivation of per and tim transcription in a cycling negative feedback loop, and activation of
dClk
transcription which participates in dCLK-CYC negative feedback loop. The
dCLK
and
CYC
form
heterodimers that activate
per
and
tim
transcriptions and inhibit
dClk
transcription. Among these five
genes, three genes,
per
,
tim
, and
dClk
, are rhythmically expressed:
per
and
tim
mRNA levels begin
to rise in the subjective day and to peak early in the subjective evening, and
dClk
mRNA level peaks
late at night to early in the morning. Although
per
and
tim
mRNAs reach peak levels in the evening,
PER and TIM levels do not peak until late evening. It is considered that this delay results from the
initial destabilization of PER by DBT-dependent phosphorylation followed by the stabilization of PER
