Tumor-Derived Vasculogenesis - Cellular Potts Models: Multiscale Extensions and Biological Applications - page 124

a gradual transition from the initial round stationary state to a migratory
bipolar morphology, with clearly distinguishable leading and trailing surfaces
dictating the direction of motion. It is useful to underline again that, also in
this bidimensional case, the polarization of migrating individuals has not re-
quired any a priori assumption or prescribed rule on their length (as done in
similar models, see [260]). As commented in the case of the single cell simula-
tions, it in fact emerges as the natural result of the interplay between the local
chemotactic-induced membrane extension at the front of the cells (impossible
with the homogeneous chemical strength used in those approaches, as already
commented) and the mechanical properties given to their compartments, with
a stiff nucleus and a more fluid cytoplasm.
The model also allows an accurate analysis of intracellular calcium events
during the overall tubulogenic process. In particular, as depicted in Figure 7.6,
the simulations show that VEGF-evoked Ca 2+ signals are clearly detectable
in the early phases of the patterning, when TECs are not well connected in
a mature network, while when the tubules are more structured they are sig-
nificantly downregulated. The peculiar temporal evolution of calcium signals
has been observed also in in vitro assays [133] and may play a specific role
in transducing information during the different phases of the process [282].
In this regard, even though experimental models have not yet shed light on
the molecular mechanisms underlying such a decay in calcium events, our
approach could suggest a simple and plausible functional explanation. The
initial dramatic increase in intracellular calcium levels is in fact necessary for
the enhancement of cell migratory properties, which is in turn fundamental
in the first stages of the patterning, as TECs have to eciently move and
interact. Subsequently, when the network is mature, the positions of cells are
stabilized in the structure and, without the necessity of a significant further
locomotion, their migratory capacities can be partially inactivated and, there-
fore, the cytosolic Ca 2+ can decrease until almost its basal level. It is useful
to notice that the use of a constant chemotactic strength (i.e., as in classical
CPMs) would have unrealistically affected the stabilization of the structure,
since the cells would have continued to move following the external chemical
stimulus, likely detaching from each other. The regulation of Ca 2+ -dependent
mechanisms may thus represent an important target for therapeutic strate-
gies, which aim at disrupting malignant vascularization and, eventually, at
inhibiting tumor development as experimentally provided in [284, 306].
7.4 Varying Cell Density
Up to now we have shown the model ability to start from realistic initial data
and foresee the dynamics of tumor tubulogenesis consistently with respect
to published experimental works. We now focus on the pattern dependence