Biomedical Engineering Reference
In-Depth Information
A calcium-dependent elasticity of the cell cytosol, in conjunction with the
presence of a rigid nucleus and of a local chemical stimulus, constitutes there-
fore a sucient set of minimal and simplified requirements for a cell transition
from a symmetric stationary morphology to a polarized mobile state. Obvi-
ously, a more realistic model should explicitly include the dynamics of the cell
cytoskeleton and its signal transduction (this topic, often approached in the
literature with multiphase models, see for example the topic [77], could rep-
resent a fundamental improvement of CPM applications, since it has received
little though increasing attention). In fact, the proposed approach does not
focus on the dynamics of actin filaments, but rather considers the cell cytosol
as a single elastic body undergoing local mechanical stresses, due to ther-
modynamical forces and chemical stimuli, on its membrane. A more detailed
multiscale model would combine both approaches, using the stress distribu-
tions at the PM as a signaling input for the subsequent polimerization process
of the actin cytoskeleton. The introduction of the cell cytoskeleton dynamics
would result also in a more accurate description of the movement of cell nu-
cleus, which is in fact mediated by the interactions with the matrix substrate,
via intermediate filaments and microtubules. These could be more realistically
described by an explicit model of the actin component of the cell cytoskeleton.
However, the assumptions made do not strongly influence the final out-
comes of the model. The dynamics of the nucleus are in fact kept constant in
all the proposed sets of simulations by fixing the value of its stiffness,
volume
;N
and
surface
;N
, and of its mobility, T
;N
. In this way, the migratory properties
of the TEC are mainly determined by the other mechanisms involved (such
as molecular processes), which instead vary in each case.
The importance of the compartmentalized approach is also underlined by
studying the phenomenology of the cell in the case of a monocompartmental
representation (i.e., the TEC is formed by a single, undifferentiated cytoplasm,
while all the other model assumptions are not changed). As reproduced in
Figure 6.6(C), the polarization process does not emerge and the cell is a
deformed mass which moves in the direction of the chemical source (notice
that also the top of the cell unrealistically protrudes).
For a quantitative characterization of cell motility, we define cell average
directional displacement and velocity (i.e., along the x-axes, in the direction of
the chemical source), which facilitate the comparison between the analyzed ex-
perimental conditions. In particular, the cell directional displacement is simply
the x-coordinate of the cell center of mass at a given time, while the direc-
tional velocity is the relative component of its average velocity, v
x
= (v
CM
)
x
dened as in Equation (1.12), where t = 60 MCS, and thus 10 min.
After an initial stage, when the cell is still round and does not strongly
sense the VEGF stimulus, the directional velocity rapidly increases until it sta-
bilizes at 42 m/h (when the EC is completely polarized); see Figure 6.7(C,
left panel). This agrees with the range of speeds measured in [309] for real
ECs in embryonic mouse allantoides (28{40 m/h). In particular, the cell ve-
locity has been therein evaluated relative to the motility of the surrounding
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