Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 174

by an arbitrary factor of 1.28. The secretion of the proteolytic enzymes by the tip
cell is kept constant at a maximal rate.
We study how u-PA and MMP secretion by stalk cells affects sprout mor-
phology. Figure 6 gives an overview of the simulation results as a function of the
secretion rates of u-PA and MMP. Because the simulations are stochastic, varia-
tion is seen between simulations with the same parameter settings; representative
simulations were selected for the morphospace in Fig. 6 . Sprout morphology can
be grouped in four categories: sprouts, solid round cysts, hollow cysts and mon-
olayers. Sprouts have a cord-like orientation of cells, while cysts are more round
and multi-cellular. A high secretion of both u-PA and MMP (Fig. 6 d) by stalk cells
results in lowering of the monolayer. Sprouts are formed for low secretion of u-PA
(Fig. 6 a), while solid cyst-like structures are formed for medium levels of u-PA
secretion (Fig. 6 b) for all MMP secretion levels by stalk cells. High secretion of
u-PA and low secretion of MMP (Fig. 6 c) results in hollow-cyst like structures.
Occasionally (6 out of 128 simulations), no sprouting occurs for low levels of
MMP secretion by stalk cells because stalk cells position themselves between the
tip cell and the BM and thereby prevent degradation of the basement membrane.
An interesting transition is seen between a hollow cyst-like structure and mono-
layer lowering for a secretion of MMP between 8 and 12 %. The hollow cyst-like
structures can be formed since the BM remains intact for attachment of endothelial
cells before this transition. These structures are likely to collapse if gravity was
included in the model. Experimentally, tubular structures can also disappear due to
excessive fibrinolysis [ 43 ].
u-PA can activate MMP, thus the activity of both enzymes are likely to increase
simultaneously. The sprout morphologies that are seen along diagonals of the
morphospace in Fig. 6 are therefore biologically most probable. Along the diag-
onal, we see sprout formation for low secretion of both enzymes by stalk cells, cyst
formation for medium secretion and monolayer lowering for high secretion. This is
consistent with the experimental results by Collen et al. [ 43 ] and our own
hypothesis as discussed above. The intensity and the distribution of proteolytic
enzyme secretion over different cell types (tip and stalk cells) thus seems to be a
sufficient explanation for the tissue behavior observed in the laboratory.
The computational model is oversimplified, because it only describes proteo-
lytic activity at the membrane and no diffuse matrix degradation or inhibitors. The
notion that TNFa induces secretion of proteolytic enzymes as well as their
inhibitors implicates a more complex regulation of matrix degradation during
sprouting. Lowering of the endothelial monolayer, when exclusively stimulated
with angiogenic factors, is likely to depend on soluble rather than membrane-
bound proteolytic enzymes. Inhibitors and soluble proteolytic enzymes should be
included to understand the basic principles of angiogenesis.
Beside proteolytic degradation of the extracellular matrix, it is likely that the
structure of the matrix influences tube formation. Matrix structure for example
effects the sensitivity of fibrin matrices to proteolytic degradation [ 43 ]. The
composition of fibrin matrices can be controlled experimentally [ 47 ]. High
molecular weight (HMW) and low molecular weight (LMW) fibrinogen can be