Biomedical Engineering Reference
In-Depth Information
volume or surface attributes. In particular, we neglect cell{matrix interac-
tions or matrix remodeling mechanisms, such as the secretion of protein or
degrading enzymes.
The system Hamiltonian is given by
H(t) = H
constraint
(t) + H
adhesion
(t):
(5.1)
H
constraint
includes the constraints regulating cell volume and surface which,
in two dimensions, correspond to the cell area and perimeter. They have the
same form as in Equation (4.6). The cell target dimensions, given in Appendix
C, correspond to their initial measures, which reflect the most common mor-
phologies observed in classical cultures of ARO cells [101] measured in [349].
Cells are not seen to grow during an experimental wound healing assay [101]
and, as already seen in Section 2.1, HGF/SF stimulation does not cause a
dramatic cytoskeletal reorganization: therefore, it is not restrictive to assume
for any cell and any unit
high constant values of
8
<
surface
;N
=
surface
;C
=
surface
;M
;
:
perimeter
;N
=
perimeter
;C
=
perimeter
;M
:
H
adhesion
is straightforwardly differentiated into internal and external contact
energy contributions, cf. Equations (4.1), (4.2), and (4.3). In particular, J
ext
E;E
is related to the capability of cells and
0
of creating local intercellular
cadherin{cadherin complexes that are downregulated by the activation of Met
receptors. Hence, adopting the same notation used in Section 4.3, for any ARO
and for (
(
x
)
) = M, we obtain that
;
(x;t) = s
J
ext
;I
s
J
ext
(x;t) = (m(x;t)):
;
Therefore, for any couple of neighboring cells and
0
we have the following
local relation (at the interface (@x 2 @) \ (@x
0
2 @
0
)):
E;E
(s
J
ext
;I
(x;t); s
J
ext
;I
J
ext
E;E
((@x 2 @) \ (@x
0
2 @
0
);t) = J
ext
0
;
0
(x
0
;t)) =
;
= g
J
ext
(s
J
ext
;I
;
(x;t); s
J
ext
;I
0
;
0
(x
0
;t)) = J
0
exp(km(x;t)m(x
0
;t)):
The coecient J
0
represents the adhesive force between resting AROs: it is
a low value, qualitatively reproducing the high contact interactions between
unstimulated AROs that, in the absence of external stimulations, tend to
remain closely packed in circular islands, as it is possible to appreciate in the
representative experimental images in [101, 349].
The above relations reproduce the fact that Met activation induces the
local disruption of cell{cell adhesion junctions by the dispersal of E-cadherin
and -catenin from the intercellular complexes [101]. It is noteworthy that
the basic CPM, without the compartmentalization technique, could have not
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