Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 167

highly motile cells. To move away from the mother vessel and form a sprout, cells
must migrate against a steep gradient of self-secreted chemoattractant. Once a
small sprout is created by a motile cell, the gradient around this outgrowth is less
steep than the rest of the gradient, so cells within the sprout have higher motility
than elsewhere, causing an instability.
Although most of the previous models simplified angiogenesis by assuming
endothelial cells all have identical properties, in fact differentiation between
leading ''tip'' cells and following ''stalk'' cells is key to sprouting angiogenesis.
Bentley et al. [ 12 ] investigate the molecular and biophysical mechanisms driving
tip and stalk cell differentiation using an agent-based, computational model [ 12 ].
The model represents a row of cylindrical endothelial tip and stalk cells made up
of multiple agents. Only the tip cells can extend filopodia outwards, representing
an new sprout as shown in Fig. 2 f. The model is used to study the interaction
between Dll4-Notch1-signaling with VEGF-induces tip cell activation [ 28 ]. The
robustness of tip cell selection is investigated by applying a VEGF gradient per-
pendicular to the vessel [ 29 ]; each cell senses the same level of VEGF, which
combined with a Dll4-Notch1-based lateral inhibition mechanism produces a
pattern of alternating tip and stalk cells. The tip cells grow long filopodia that may
meet up to form a connected vessel; anastomosis. When the common surface area
of the connecting tip cells has increased sufficiently, one of the two cells becomes
a stalk cells and the vessel stabilizes. Thus, the model suggests that the common
surface area is a determining factor for tip cells selection; if the common surface
area is too small lateral inhibition does not work. A second application of the
model involved cellular competition for the tip cell position. Time-lapse micros-
copy has shown how stalk cells migrate along the sprout, take up the role of tip
cell, and inhibit the original tip cell become a stalk cell [ 30 ]. Cell variants with
higher levels of VEGFR2-expression have a competitive advantage over the wild-
types: they end up more often at the tip of the sprout, but only if Notch1 can inhibit
Dll4 expression. The advantage of the variants diminishes when all cells have low
levels of Notch1. These observations suggest that Notch limits the levels of
VEGFR2 in wild-type cells. Bentley tests this hypothesis in her agent-based
angiogenesis model by applying a VEGF gradient along the sprout and by
allowing cells to switch places. Switching is regulated the level of VEGFR2 and
Notch expression; VEGFR2 promotes switches towards VEGF while Notch1
inhibits the same switches. With these assumptions the experimental observation
could

be reproduced, suggesting that this mechanism may explain tip cell

shuffling.

2.3 The Future of Angiogenesis Modeling

The models discussed so far, all isolated specific aspects of angiogenesis to predict
the outcome of proposed in vitro experiments. To study angiogenesis in vivo, we
must incorporate the interaction with the rest of the body in a multi-scale model.