Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 169

Fig. 3 A schematic cross-
section of the experimental
model by Koolwijk et al. [ 1 ].
Endothelial cells are seeded
on a three-dimensional fibrin
matrix and form capillary-
like tubular structures upon
stimulation
structures (e.g. cell membranes) and cell behaviors (e.g. cell-cell adhesion and
pseudopod extensions). These models are intuitive and relate well with biological
observations. To illustrate the approach, we created a computational cell-based
model of an in vitro model of capillary-like tube formation, introduced by
Koolwijk et al. [ 1 ].
A schematic representation of a cross-section of the experimental model is given
in Fig. 3 . A monolayer of isolated human microvascular endothelial cells (hMVEC)
is seeded on a three-dimensional fibrin matrix. The composition of this matrix,
consisting of only fibrin (Fig. 7 ), is completely controlled and reproducible. The
endothelial cells grow into the matrix and form capillary-like tubular structures upon
stimulation with an angiogenic factor, VEGF and/or bFGF (basic fibroblast growth
factor), in combination with the inflammatory mediator TNFa (tumor-necrosis factor
alpha). TNFa is suggested to induce receptor-bound u-PA (urokinase-type
plasminogen activator) activity to enable the cells to degrade the fibrin matrix [ 38 ].
Although VEGF and bFGF are both growth factors, TNFa completely inhibited the
growth factor-induced proliferation in this experimental model.
The computational model of sprouting is designed to be easy to relate to the
experimental observations. The model can be used to explain and predict angio-
genic patterning on tissue level, based on quantitative descriptions of cell
behavior. The most important cell behaviors, such as cell shape, cell adhesion and
haptotaxis are therefore included, and their effects and relative importance in
sprouting can be examined. Endothelial cells have a wide range of interactions
with the extracellular matrix, of which the function as well the effects are often
still unclear. Endothelial cells for instance secrete proteolytic enzymes to degrade
the matrix. The proteolytic activity is regulated by a complex system and the
computational model can help to gain insight in the relative importance of
the components in this system, in the regulation of the system and in the effect of
this regulation on sprouting.
3.1 Computational Sprouting Model
To mimic the experimental set-up of Koolwijk et al., the computational model
starts with a monolayer of cells, of which one is a tip cell and the rest are stalk
cells, on a fibrin matrix and a basement membrane (BM) in between. The Cellular