Biomedical Engineering Reference
In-Depth Information
Figure 3
. (
a
) The model scheme is an abstraction of the PI cycle shown in Figure 2. (
b
) Initial
dynamics of the membrane phosphoinositides at any point of the cell membrane. The initial
concentrations of active receptors, S, and inositol phosphates, J
-
, are treated as control parame-
ters. When S is small or J
-
is large, there is a threshold (defined as the distance between the
lower and intermediate steady states). As S increases or J
-
decreases, the threshold becomes
progressively smaller. At sufficiently large values of S or sufficiently small values of J
-
, the
threshold disappears completely.
4. The receptors instantly inherit the chemoattractant profile imposed on the
cells, and the receptor-mediated rate of formation of membrane phosphoinositi-
des per unit length of membrane is given by
r
p,f
k
f
r
(
t
,R)
p
2
p
s
.
Here,
k
f
denotes the rate constant and
r
(
t
,R) denotes the concentration of active
receptors. The dependence on
p
2
represents the autocatalytic and cooperative
kinetics with respect to membrane phosphoinositides. This is an idealization of
the positive feedback loops shown in Figure 3a. Thus, the membrane phospho-
inositides will play the role of
local activator
in the model.
5. The inositol phosphate pool (
I
) stimulates transfer of phosphoinositides
from the plasma membrane to the endoplasmic reticulum. Thus, the rate of re-
moval of membrane phosphoinositides per unit length of the membrane is
r
p,r
k
r
pi
,
where
k
r
denotes the rate constant. The rationale for this assumption is as fol-
lows. Inositol participates in the regeneration of PI in the endoplasmic reticulum
(Figure 3a). An increase in inositol concentration will, therefore, drive the trans-
port of PA from the plasma membrane to the endoplasmic reticulum and its sub-
sequent conversion to PI. Thus, the inositol phosphates act as a
global inhibitor
.
To simulate the experiments, it is assumed that before the cell is sub-
jected to a chemoattractant perturbation (
t
< 0), it is at a homogeneous steady
