Biomedical Engineering Reference
In-Depth Information
FIGURE 1.3: Illustrative simulations of the biological role of the adhesive
energies. In a 200 200-site domain , a round cluster of cells is placed.
The cells are all of the same type, with an initial diameter of 8 sites, target
measures A
surface
C
and A
perimeter
C
equal to the initial dimensions,
surface
C
=
50 site
2
, and
perimete
C
= 0:2 site
1
. The final configurations correspond to
J
C;C
= 0:4 J
C;M
= 25 (left panel); J
C;C
= J
C;M
= 4 (middle panel); and
J
C;C
= 25 J
C;M
= 0:4 (right panel).
notice that similar dynamics can he obtained in the three-dimensional case by
substituting, respectively,
surface
with
volume
and
perimeter
with
surface
.
As stated above, the values of the binding energies Js in Equation (1.5)
describe the relative preference of simulated individuals for creating adhe-
sive homotypic (i.e., with individuals of the same type) or heterotypic (with
individuals of other types or with extracellular components) boundaries. To
analyze how specific variations of such adhesion strengths affect the overall
dynamic, as well as the final configuration, of a biological system, we first ex-
amine the evolution of a round cluster of cells, all of the same type (
) = C,
plated in the center of the standard extracellular medium, = M; see Figure
1.3. For the sake of simplicity, the cell initial and target measures coincide,
with a high surface constraint
surfac
C
1 that preserve their dimensions
and a low perimeter constraint
perimeter
C
1 that allows their remodeling
and fluctuations.
If J
C;C
J
C;M
, which means an intercellular adhesion significantly higher
than the cell{medium adhesion, and hence either an overexpression of cadherin
molecules or a downregulation of integrin ligands, the cellular spheroid remains
compact and strictly packed, trying to minimize its external surface, because
for the cells it costs more, from an energetic viewpoint, to float in the medium
rather than stay attached to each other (Figure 1.3 (left panel)).
If the two contact energies are instead comparable (i.e., J
C;C
J
C;M
), a
small friction with external cells is able to randomly detach and reattach from
the rest of the cluster, whose overall border continuously remodels (Figure 1.3
(middle panel)).
Finally, for larger values of cell{cell adhesion (i.e., J
C;C
J
C;M
, which
represent the model counterpart of downregulation in cadherin activity), the
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