Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 163

implemented, network formation only occurs for narrow parameter ranges:
strongly adhering cells or steep chemical gradients [ 22 , 23 ]. Therefore, Merks
et al. proposed two hypotheses for which network formation occurred for a much
wider range of parameters: contact inhibition [ 14 ] and cell elongation [ 13 ].
The contact inhibition hypothesis proposes that cells only respond to the
autocrine chemoattractants where the cell membrane is not in contact with other
cells. This exclusive sensing is thought to be mediated through the dual function of
VE-cadherin; it acts as a homophilic trans-membrane cell-adhesion molecule and
it plays an inhibitor role in the VEGF signaling pathway [ 24 ] which increases cell
motility. Contact-inhibition locally reduces the cell motility. Therefore, cells
within the cluster do not respond to the chemoattractant that all cells secrete. This
process appears to contribute to both network formation (Fig. 1 d) and sprouting
angiogenesis. The reasons for this are best understood in the context of sprouting
angiogenesis and will therefore be discussed in Sect 2.1 .
The cell elongation hypothesis is based on the biological observation that cells
elongate during network formation. In this model, the combination of elongated
cells with autocrine chemotaxis results in network formation [ 13 ]. The final net-
work, which can be observed in Fig. 1 e, is similar to in vitro networks. When cell
elongation is omitted, the cells aggregate instead of forming network, indicating
that cell elongation drives network formation in this model. The evolution of
network properties over time, such as the number of nodes and meshes, correspond
with data from in vitro experiments with HUVECs on Matrigel. This suggests that
cell elongation may play an important rule during network formation. In this
model network formation occurs at two time-scales. First, cell elongation induces a
persistent movement along the long axis of the cell. This causes the formation of
thin branches of connected cells. Second, the network coarsens by fusion of
branches and mesh collapse. This is driven by the chemotaxis that enables slow
migration of cells along their short axis.
An alternative hypothesis was proposed by Szabó et al. [ 7 , 9 , 10 ]. Their
experiments suggested that neither mechanical interactions nor chemotaxis are
required for network formation [ 7 ] and that cells move preferential towards elon-
gated cells. From these observation they propose that network formation is driven
by the preferential attraction to elongated structures. This hypothesis has been
used as a basis for both a particle based model [ 7 ] and a cell-based model [ 9 , 10 ].
In the particle based model cells are represented by point particles that diffuse and
adhere to their neighbors. While this model lacks some key cell properties,
including cell shape, it suffices as a proof-of-concept model for preferential
attraction to elongated structures. The models are used both to investigate network
formation from dispersed cells [ 9 ] and sprouting from a blob of cells [ 10 ]. This
model suggests that cells can indeed form network only due to cell-cell interactions,
as is shown in Fig. 1 f. Sprouts formed in these networks only become stable when
they connect to other sprouts, suggesting that anastomosis stabilizes the formed
network.
Because they all produce similar morphological patterns, none of the modeled
hypotheses can be ruled out as a driving force for network formation. Cell-based