Biomedical Engineering Reference
In-Depth Information
smaller the number of total receptors in a cell, the more pronounced the stochas-
tic effects. If we define the dimensionless variables
t
r
r
k sp
U
w
,
S
=
i
,
S
=
m
,
X
=
W
r
t
,
(
)
i
m
i
i
1/
ksp
r n
/
r n
/
r n
/
r
t
t
t
t
and the dimensionless parameters,
l k
kk kp
,
M
=
,
L
=
r
/
+
t
and equation [12] becomes
¯
(
)
(
)(
)
(
)
d
SLM SSULMSSX
=+
1
d
+
1
+
d
,
i
=
1,2...
n
.
[13]
¡
°
¢
±
i
m
i
m
m
i
To simulate the experiments showing spontaneous polarization, it is as-
sumed that at U = 0 the cell is exposed to a small and uniform chemoattractant
concentration, M = M
-
. At U 0, the cell is immersed in a uniform concentration
of chemoattractant M
+
> M
-
. Euler integration of equation [13] yields a noisy ac-
tive receptor distribution, a typical snapshot of which is shown in Figure 6a. The
response to stochastic receptor-ligand binding is then simulated by choosing this
noisy active receptor distribution as the function S(U,Y) in model equations [6]-
[8]. The simulation shows that the sudden increase from M
-
to M
+
causes an initial
uniform increase in membrane phosphoinositides, but this is followed by the
formation of a phosphoinositide peak at a random location (Figure 6b).
Figure 6
. Spontaneous polarization in response to a uniform but noisy chemoattractant profile:
(
a
) a snapshot of the noisy active receptor distribution generated by the Tranquillo-
Lauffenburger model, and (
b
) development of a phosphoinositide peak in response to this
noisy signal.
