Biomedical Engineering Reference
In-Depth Information
Figure 4
. Amplification of a small chemoattractant gradient: (
a
) distribution of active recep-
tors at
t
0, (
b
) development of a pronounced membrane phosphoinositide peak at the lead-
ing edge of the cell at Y = 1/2, (
c
) growth of the uniformly distributed inositol phosphate pool.
to the upper steady state only if it crosses the unstable steady state. If S is large
at a point, the threshold disappears at that point, and every Q, no matter how
small, tends to move toward the upper steady state. Now, at time
t
< 0, S = S
-
everywhere and there is a threshold at every point. Upon activation of receptors
at
t
= 0, S becomes significantly large in a neighborhood of the leading edge. In
this region, the threshold vanishes and the concentration of
P
starts growing.
Although
P
diffuses slowly, it does have a tendency to spread throughout the
cell membrane. This tendency is contained by the formation of cytosolic inositol
phosphates (
I
), which rapidly diffuse away from the leading edge, and acquire a
relatively flat profile. The rapid diffusion of
I
has a twofold effect. In the
neighborhood of the leading edge, the inhibitory effect of
I
is diminished, so that
localized growth of the phosphoinositide peak increases. Outside this neighbor-
hood, the higher concentration of
I
promotes transfer of membrane phospho-
inositides from the plasma membrane to the endoplasmic reticulum. The net
effect of this transfer is to deplete the plasma membrane of its phosphoinositi-
des, thus preventing the peak from spreading beyond the leading edge. Hence,
within the leading edge, the steady-state concentration of
P
is higher than the
initial basal level. Outside the leading edge, it is lower than the initial basal
level.
2.2.2. Polarized Sensitivity
The model has also been used to explore the phenomenon of polarized sen-
sitivity. To this end, the model cell is exposed to a chemoattractant gradient and
allowed to form a steady-state phosphoinositide peak consistent with this gradi-
ent. After the steady state has been reached, the polarized cell is subjected to a
new chemoattractant gradient that is different from the previous gradient. The
