Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 173

degrade the basement membrane. The production and activity of u-PA and MMPs
is interlinked; u-PA activity is suggested to induce MMP activity indirectly and at
least one membrane-bound MMP (MT1-MMP) is known to be capable of fibrin
degradation as well [ 44 ].
Proteolytic activity can be manipulated by stimulation of the cells with angio-
genic factors or inflammatory factors [ 43 ]. To induce sprout formation, low
amounts of TNFa are added to the monolayer of endothelial cells in combination
with a growth factor. Stimulation with angiogenic factors alone induces a uniform
degradation of fibrin and the monolayer of endothelial cells does not sprout but as a
result lowers as a whole. This uniform degradation of fibrin can result from a
combination of diffuse proteolysis induced by the angiogenic factors and the
absence of inflammatory factor induced inhibitors of proteolysis. Excessive plas-
minogen activation, in endothelial cells seeded in suspension into a three-dimen-
sional fibrin matrix, results in the formation of round cyst-like structures [ 45 ]. Cyst-
like structures are also observed in the endothelial monolayer model [ 1 ] after
stimulation with a higher dose of TNFa in combination with angiogenic growth
factors by Koolwijk et al. (data not shown).
We aim to find the conditions that suffice to explain the experimental obser-
vations on sprout morphology. This hypothesis will then be tested with the
computational model. We hypothesize that the intensity of proteolytic enzyme
secretion (u-PA and MMP) as well as the distribution of secretion over different
cell types is responsible for the observed phenotypes in angiogenesis. After low
stimulation with TNFa ; tip cells might already secrete proteolytic enzymes at
maximal rate and are therefore insensitive to stimulation. In contrast, stalk cells
normally do not secrete many proteolytic enzymes and are therefore more sensi-
tive for stimulation than tip cells. Indeed, the tip cell was seen to have the most
u-PA receptors during sprouting, which facilitate proteolysis to degrade fibrin [ 46 ].
When both tip and stalk cells secrete high levels of proteolytic enzymes, the fibrin
will be degraded uniformly.
To test this hypothesis in the computational model, we assumed that both tip
and stalk cells can secrete u-PA and MMP. As discussed above, proteolysis is a
complex system that involves membrane-bound and soluble proteolytic enzymes
as well as inhibitors. For simplicity, only membrane associated proteolytic activity
and no inhibitors are considered in this first attempt. Since inhibitors are not
modeled explicitly, proteolytic activity and secretion of proteolytic enzymes are
directly coupled. The presence of inhibitor is modeled by lower secretion rates of
the proteolytic enzyme. To model proteolytic activity at the membrane, the dif-
fusion constants for the proteolytic enzymes are set to a very low value (Table 1 ).
Secretion of the proteolytic enzymes could also be thought of as expression of the
receptors that facilitate the activity of the enzymes at the membrane. Soluble
proteolytic enzymes are not modeled, although high secretion of proteolytic
enzymes does result in proteolytic activity at a larger distance. MMPs are assumed
to exclusively degrade the basement membrane, while u-PA degrades the fibrin
matrix. Mitosis of stalk cells is also included in the model to supply the monolayer
with new cells, simply by dividing a cell over its short axis when it has increased