Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 165

This model suggests that basic cell properties can explain the need for proliferation
in sprouting.
The model by Szabó et al. [ 10 ] describes cell shape, cell membrane and cell
migration in much more detail. The model does not consider chemotaxis or cell-
matrix interactions. The cell properties and behavior that are specific for this
model are preferential attraction to elongated structures, cell polarity and self-
propulsion (i.e. persistence of motion). The model also differentiates between tip
and stalk cells. The tip cell is polarized, causing directed movement in the
direction of the polarization vector. The results shown in Fig. 2 c suggest that both
preferential attraction and self-propulsion are necessary to reproduce realistic
sprouting behavior. Cell polarization may be regulated by cell-cell contacts and
VE-cadherin may be a key player for this. Moreover, the model suggest that
differential behavior at the tip of the sprout may drive sprout formation. Therefore,
this model suggests that proliferation may not be required, as long as the supply of
cells from the main vessel is sufficient.
Cell-matrix interactions The previous two cell-based sprouting models have
only considered cell properties and cell behavior, ignoring all ECM and stromal
tissue. Anderson and coworkers [ 6 ] created a particle based, hybrid model
describing sprouting angiogenesis. In this model cells are represented as point
particles on a grid while the chemotactic and haptotactic fields are still described
as continuum equations. This model was used to investigate how the balance of
haptotaxis and chemotaxis influences branching and anastomosis. As shown in
Fig. 2 b branching and anastomosis occur in the model, but these behaviors only
occur when cells are able to move perpendicular to the chemotactic field, which is
enabled by haptotaxis. When the haptotactic forces are strong enough branches can
split and reconnect in order to form a functional vasculature.
Anderson et al. model [ 6 ] suggests that haptotaxis is key to branching, but it did
not show how cells interact with their heterogeneous environment. A more recent,
cell-based model, represents the ECM as a static, heterogeneous configuration of
matrix fiber bundles, interstitial fluid and immobile tissue-specific cells [ 11 ]. The
endothelial cells in the model are motile and adhere stronger to matrix fibers than
to the surrounding matrix. Immobile cells act as obstacles that hinder the migration
of endothelial cells. The tip cell is influenced by a chemoattractant field and it
degrades ECM components. Degradation of the extracellular matrix during
sprouting enables cells to migrate and branch off the main sprout as shown in
Fig. 2 d. The model suggests that a heterogeneous composition of the matrix is
necessary for the formation of branches; the inhomogeneities in the matrix enable
cells to split from the main branch. Furthermore, the model suggests that the
proliferation region determines sprouting dynamics but does not affect the final
sprout morphology.
A follow-up model was used to investigate cell-ECM interaction in more detail
[ 27 ]. In this model all cells respond to the chemoattractant and that the immobile
tissue cells are removed, ie, only fibers cause matrix heterogeneity. The model
suggests that sprouting only occurs in a specific range of matrix densities, which
corresponds with experimental observations. Moreover, simulation results suggest