Biomedical Engineering Reference
In-Depth Information
by p) and MAPK (k) molecules:
@p
@t
=
D
p
r
2
p
p
p;0
+
| {z }
Metinduced production
p
p
|{z}
decay
+
;
(5.5)
| {z }
diffusion
@k
@t
=
D
k
r
2
k
k
k;0
+
| {z }
Metinduced production
k
k
|{z}
decay
+
:
(5.6)
| {z }
diffusion
The diffusion coecients, D
p
and D
k
, and the degradation rates,
p
and
k
, are assumed to be constant and homogeneous within the cell cytosolic
compartment, and are taken from theoretical works presented in [210, 243,
255]. The third terms in Equations (5.5) and (5.6) describe the production of
the chemicals in the sub-plasmamembrane region, triggered by Met receptors,
as for (
(
x
)
) = C and (
(
x
0
)
) = M
(x;t) =
X
x
0
2
0
x
m(x
0
;t):
(5.7)
In the absence of specic determinations for AROs, the Michaels{Menten co-
ecients
k
and
k;0
are chosen to reproduce the curve of the HGF/SF-
dependent MAPK phosphorylation provided for retinal endothelial cells
(RECs) in [60].
p
and
p;0
are instead estimated to fit the maximal amount
of phosphorylated PI3K at a given concentration of HGF/SF, which has been
measured in the same article.
Finally, the intracellular quantities of activated Cdc42 (c) and Rac (r) are
regulated, respectively, by the equations
@c
@t
=
D
c
r
2
c
c
c
|{z}
decay
+
p
c
p
| {z }
PI3Kinduced activation
+
k
c
k
| {z }
MAPKinduced activation
;
| {z }
diffusion
(5.8)
@r
@t
=
D
r
r
2
r
r
r
|{z}
decay
+
p
r
p
| {z }
PI3Kind: act:
+
k
r
k
| {z }
MAPKind: act:
+
c
r
c
| {z }
Cdc42ind: act:
;
| {z }
diffusion
(5.9)
where the diffusion and decay rates are constant within the entire cell (i.e.,
(
(
x
)
) 2 fC;Ng). The third and forth terms in Equation (5.8) describe
the cytosolic (i.e., p and k do not diffuse in the nuclear region) activation of
Cdc42 mediated by PI3K and MAPK, at constant rates
pc
and
kc
. In the
literature, there are no available values for such parameters. However we set
pc
<
kc
, to describe a stronger dependency of Cdc42 on MAPK and a
weaker dependency on PI3K. This is biologically consistent as PI3K activates
Cdc42 only in a direct way, while MAPK interacts with the G-protein through
distinct pathways [386]. The analogous terms in Equation (5.9) reproduce the
triple regulation, by PI3K, MAPK, and Cdc42, on the activation of Rac at
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