Figure 1.
Schematic illustration of the cancer network involving miR-17-92, E2F, and Myc.
and
denote the protein module (Myc and E2Fs) and the miRNA cluster, respectively.
Figure 2.
Steady-state bifurcation diagrams of the dimensionless protein concentration
(top panels) and phase diagrams (bottom panels) of switching behavior. The strength of the dimensionless measure of miRNA inhibition
is increased from
to
,
and
(from left column to right one). In the bottom panels, the red dashed lines denote the range of the protein expression constant
, from
to
. Clearly, the system is greatly improved with regard to the ability of the toggle switch with the inclusion of miRNA inhibition
. Here,
.
Figure 3.
The dynamical behaviors of the system when increasing the inhibition of miRNA
. The strength of positive feedback is set at
, and the strength of negative feedback
is increased from 1.0 to 1.2 and 1.6 from left to right. Parameter
and
. The upper rows show the time course of the
response to (A and B) the pulse input,
for
and
for others, or (C) a constant stimulus with
, where the red dashed lines denote the input signal. The lower rows show the corresponding bifurcation diagram, where
/
denotes saddle point and
/
represents a Hopf bifurcation. Clearly, the system undergoes transitions from bistability to excitability and to relaxation oscillation with increasing
.
Figure 4.
Bifurcation diagram in the space spanned by
and
with
,
. The bulk diagram of the dynamical behavior of the system is composed of four regions: monostability, bistability, excitability, and undamped relaxation oscillation. The red and blue circles on borderlines denote the saddle-node and Hopf bifurcations, respectively.
Figure 5.
Responses of switches to a step stimulus input.
(A) The jumping stimulus input from to
at time
. (B) The responses of the system for a fast loop
(red) and a slow loop
(blue), where
. (C) The same as (B) but with
. (D) The same as (A) but with an imposed fluctuation
, where
is Gaussian white noise with variance
and mean
, and
is the same as in (A). (E–F) The same as (B) and (C), respectively. All simulations used
and
.
Figure 6.
Time course of fluctuation-induced escape from the on-state (upper state) to the off-state (lower state).
Each time course represents the evolution of the fraction that has transitioned at least once to the off-state, for an ensemble of
cells. Here, the parameters are
,
,
,
, and a Gaussian white noise with variance
.
Figure 7.
Noise tolerance and response features of the systems including the inhibition of miRNA.
(A) Steady values of the fraction of transition from the initial on-state to the off-state as a function of
for
. (B) The same as (A) for
. (C–D) The response time
vs
for
and
, respectively. All of the simulations used
,
, and a Gaussian white noise with variance
.