Biomedical Engineering Reference
In-Depth Information
()
cp k
/
D C
/
2
p
r
p
i
i
t
Z
w
L
w
i
E
w
i
S
w
Q
w
Q
w
s
J
w
sp
,
i
i
i
s
ksp
ksp
ksp
r
p
p
r
t
r
t
r
t
t
t
t
t
where
C
denotes the circumference of the cell and
r
t
denotes the total number of
receptors. Thus, we arrive at the dimensionless equations
s
Q
s
2
Q
=
LSQQ QJ Z LQ E
2
+
+
,
[6]
f
s
p
p
p
s
U
s
Y
2
2
s
Q
s
Q
(
)
s
=
LSQQ QJ Z LQ E
2
+
+
s
,
[7]
f
s
p
p
p
s
U
s
Y
2
s
s
J
s
2
J
2
=
LSQQ QJ Z LJ E
+
+
,
[8]
f
s
i
i
i
s
U
s
Y
2
with initial conditions
() () ()
QYQQ Y QJYJ Y
0,
=
,
0,
=
1
,
0,
=
, 0
b
<
1
[9]
s
and periodic boundary conditions
()()
() (
)
s
x
0,
U
s
x
2 ,
Q U
x
0,
U
=
x
1,
U
,
=
,
U
>
0
.
[10]
s
Y
s
Y
where
x
Q, Q
s
, J.
2.2. Simulations
Y) described below,
were simulated using the NAG subroutine D03PHF (43). In this subroutine, the
spatial coordinate is discretized by finite differences, the PDEs are reduced to
ODEs by the method of lines, and the resulting system of ODEs is integrated by
using a backward differentiation formula. The parameter values used in the
simulations are shown in Table 1. The rationale for the choice of parameter val-
ues can be found in (39). To facilitate comparison of the simulations with ex-
perimentally observed dynamics, it is useful to note that
k
r
sp
t
~ 1 1/sec (39).
Hence, each unit of dimensionless time, U, corresponds roughly to 1 sec.
Equations [6]-[10], along with various choices of S(U
,
