Biology Reference
In-Depth Information
Positive regulation
The DNA binding of CAP is regulated by glucose to ensure that the transcription of the lac operon
begins only in the absence of glucose. In fact, glucose starvation induces an increase in the intracellular
levels of cyclic AMP (cAMP). Transcription of the lac operon is activated with the help of CAP, to which
cAMP binds. When glucose is plentiful, cAMP levels drop; cAMP therefore dissociates from CAP,
which reverts to an inactive form that can no longer bind DNA. This regulatory mechanism by CAP
and cAMP is called positive regulation of the lac operon. Figure 4 shows an HFPN model representing
positive regulation of the lac operon.
Continuous places are used for representing the concentrations of the substances CAP, cAMP, AMP,
ADP, and glucose. Tokens in the places “CAP” (
m
4) and “cAMP” (
m
5) should not be consumed
by the firing of the transition
T
63
, since both CAP and cAMP are not lost when forming a complex.
Accordingly, two test arcs are used from the places “CAP” and “cAMP” to the transition
T
63
. The
weight of the arc from the place cAMP to the transition
T
63
is set to 100, while the weight of the arc
from the place “CAP” is 1, which was determined by manual tuning and referring to the simulation
results. After the concentrations both of CAP and cAMP exceed the thresholds which are given to these
two arcs as weights, the transition
T
63
can fire, transferring a token from the transition
T
63
to the place
“CAP site”.
In general, reactions among cAMP, AMP, and ADP are reversed. The transition
T
80
(the transition
T
82
) between the places “cAMP” (
m
5) and “AMP” (
m
11) (the places “AMP” and “ADP” (
m
12))
represents the reversible reaction together with the transition
T
79
(the transition
T
81
).
To the places
“cAMP”, “AMP”, and “ADP”, 1, 200, and 200 are assigned as initial values, respectively.
Recall that when glucose is plentiful, cAMP levels drop. This phenomenon is represented by the
inhibitory arc from the place “glucose” (
m
6) to the transition
T
80
. When the concentration in the place
“glucose” exceeds the threshold given at this inhibitory arc, the transition
T
80
stops firing.
In this model, since we suppose that CAP is produced continuously, its production mechanism is
modeled with the place “CAP” and the transitions
T
45
and
T
1
. The initial amount of the place “CAP”
is set to 5, since CAP is produced by a production mechanism independent of the mechanism being
described here.
Finally, the transitions
T
1
,
T
17
,
T
19
,
T
20
, and
T
21
represent the natural degradation of the corre-
sponding substances. Since these transitions represent only degradation and no production, no arcs are
going out from these transitions.
Negative regulation
In the presence of lactose, a small sugar molecule called allolactose is formed in a cell. Allolactose
binds to the repressor protein, and when it reaches a sufficiently high concentration, transcription is
turned on by decreasing the affinity of the repressor protein for the operator site. The repressor protein
is the product of the
lacI
gene, which is located upstream of the
lac
operon. Actually, after forming a
tetramer, the repressor protein can bind to the operator site.
By adding this negative regulation mechanism to Fig. 4, Fig. 5 is obtained. Since it is known from
the literature [Lewin, 1997] that repressor should be produced sufficiently prior to the production of
other substances, parameters relating to this negative regulation are set to faster values than other
parameters. In our model, a discrete place is used for representing the promoter site of a gene. When
the discrete place “repressor promoter”(
m
13) receives a token, the transcription of the
lacI
gene begins.
We can determine the transcription frequency by the delay rate of the transition
T
46
. Transcription and
