Biomedical Engineering Reference
In-Depth Information
Figure 7
. Variation of the steady-state phosphoinositide peaks with respect to different distri-
butions of L
f
S: (
a
) distributions of L
f
S, (
b
) corresponding phosphoinositide peaks.
Recently, we have shown that the phosphoinositide peak forms even though
the environment is macroscopically uniform because there is a certain range of
chemoattractant concentrations within which the homogeneous steady state of
the model is Turing unstable, i.e., unstable with respect to all nonhomogeneous
perturbations (40). Hence, any kind of noise drives the cell away from the ho-
mogeneous steady state and results in the formation of a phosphoinositide peak.
This property is characteristic of activator-inhibitor models (45).
2.2.4. Variation of the Phosphoinositide Peak With Respect to Kinetic
Parameters and External Signal
Figure 7 shows the variation of the steady-state phosphoinositide peak with
respect to three different distributions of the function L
f
S. We assume that these
distributions are achieved by fixing the active receptor distribution, S, and vary-
ing the parameter, L
f
, i.e., cells with progressively higher levels of PI3K or PI5K
are subjected to the same chemoattractant gradient. The simulations show that
the development of the phosphoinositide peak occurs only within a certain range
of L
f
. Even within this range of existence
1. The chemoattractant gradient required to provoke peak formation de-
creases with L
f
, and becomes zero for sufficiently large L
f
.
2. The width of the peak increases with L
f
(Figure 7).
When L
f
> 5, the peak disappears completely. At such large values of L
f
, no
initial perturbation can provoke the formation of a stable phosphoinositide peak.
Similarly, decreasing L
f
narrows the peak until at a sufficiently small value (L
f
<
2.2) peak formation cannot be induced.
These results have the following physical interpretation. The parameter L
f
is
the ratio of the characteristic velocities of phosphoinositide synthesis and re-
moval. If L
f
is small, phosphoinositide synthesis is rapidly opposed by inhibitory
