Biomedical Engineering Reference
In-Depth Information
defined a realistic relation for the local cell adhesive strength and for the local
quantity of activated Met.
Since, obviously, cells should not break into small fragments, we fix very
low bond energies J
int
C;M
. The contacts between the nucleus and the
PM within the same cell and between the nuclei and the cytosolic regions of
different cells do not occur because of the choice of interfacial energy and so
the relative terms are not taken into account. Finally, the adhesion energy
between the cell PM and the ECM is not considered since is not influenced by
the activity of the growth factor (see the considerations described in Chapter
2).
C;N
and J
int
Given the Hamiltonian, the transition probability of a spin flip has the
form of Equation (4.24). In particular, we test the model using p(T
;
(t)) =
tanh(T
;
(t)). For any cell and (
) = N, T
;
= T
;N
is a constant
low value that mimics the passive motion of the nucleus (the reader can refer
to Chapter 6 for a more detailed explanation). If (
) 2 fM;Cg, T
;
represents instead, as seen, a measure of the real motility of that is regulated
by the intracellular quantity of the activated Rac and Cdc42 molecules (see
the review article [329] and references therein). Adopting again the notation
of Equations (4.9) and (4.10), for any ARO and for (
) = C, we now
have that
s
T
;
(x;t) = s
T;A
;
(x;t) = (r(x;t);c(x;t));
1 + c
(t)r
(t)
1 + hc
(t)r
(t)
T
;
(t) = T
;
(s
T;A
;
(x;t)) = f
T
(s
T;A
;
where r
(t) =
P
x
2
r(x;t) and c
(t) =
P
x
2
c(x;t) are the total intracellular
amounts of Rac and Cdc42, respectively, and T
0
is a measure of the basal
ARO motility. T
0
is a low value, which has been qualitatively estimated by
observing the negligible migratory capacity of unstimulated ARO cultures, as
provided by wound healing assays and time-lapse video recording techniques in
[101]. The Michaelis{Menten law has been chosen to model a dose-dependent
enhancement of cell motility driven by the total intracellular level of the G-
proteins Rac and Cdc42.
Finally, for any ARO , the actual motility of the plasmamembrane is set
equal to that of the cytosolic region of the same individual, i.e., T
;M
(t) =
T
;C
(t).
It is useful to emphasize that the characterization of a intrinsic motility
specific for each single individual was not present in the basic model of the
wound healing assay proposed in Chapter 2, but is now allowed by the nested
approach introduced in the previous chapter.
;
(x;t)) = T
0
5.2.2 Molecular-Level Model
The intracellular HGF/Met-driven pathways on which the model is based are
depicted in the scheme in Figure 5.1. Although simplified, they are consistent
with the experimental literature presented in [92, 423].
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