Computational Modeling of Angiogenesis: Towards a Multi-Scale Understanding of Cell–Cell and Cell–Matrix Interactions - Mechanical and Chemical Signaling in Angiogenesis - page 177

4 Conclusion
In this chapter, we have reviewed how computational models shed new light on
questions involving network formation and sprouting. Firstly, we discussed how
computational models are used to test alternative hypotheses on the mechanisms
that drive network formation. Cellular and environmental factors in these models
are studied to predict their effects on angiogenesis. A comparison of experimental
results and these computational predictions can show which mechanisms are most
likely the driving forces of network formation. Secondly, we focused on compu-
tational models that provide new insights in the mechanisms of sprouting. These
models address questions about the regulation of sprouting, such as the necessity
and location of proliferation, dynamics of tip cell selection, and the influence of
angiogenic factors and the extracellular matrix. The discussed models use different
techniques to model cells: continuum models describe cells as densities, while
discrete models represent them as particles. The functioning of endothelial cells
depends on thousands of interacting proteins and genes. Cell-based models are
discrete models that represent the results of these gene and protein interactions by a
set of cell properties (e.g. cell and membrane size) and behaviors (e.g. adhesion and
chemotaxis), suggesting that a few cell behaviors sometimes suffice to explain
complex collective cell behaviors like angiogenesis [ 21 ].
To illustrate this approach in more detail, we discuss a cell-based model to
study angiogenic sprouting. This computational model is based on an in vitro
model of sprouting in a fibrin matrix by Koolwijk et al. [ 1 ]. The model is used to
formalize the mechanisms that are minimally required for sprouting and it predicts
the effects on the dynamics of tube formation of varying cell properties, such as
matrix degradation. Predictions from the model can lead to new insights and drive
experimental research. The observations and results from the experimental
research are crucial for the validation and further development of the computa-
tional model. A focus point for further study is the interaction of endothelial cells
with the extracellular matrix. Various interactions with the matrix strongly influ-
ences sprouting, but it is difficult to separately study them experimentally. We plan
to model the extracellular matrix itself and its interactions with endothelial cells in
more detail and extend our model to a multi-scale model, including molecular,
cellular and tissue levels, to gain insight in these interactions. In a close cooper-
ation between experimental and computational biologists, we can reach a thorough
understanding of how the interactions between multiple levels of organization lead
to counterintuitive effects, which experiments alone would not unveil.
Multi-scale modeling is thought to be the next step in computational modeling. If
different scales and their interactions are modeled simultaneously, we can identify
the global and local (side) effects of a therapeutic drug. Some multi-scale models of
angiogenesis have already been developed [ 32 - 37 ], as discussed in Sect. 2 . So far,
many of these models are based on phenomenological rules and the results are direct
results of the implemented rules. In order to make the step to explanatory rather than
descriptive multi-scale models, a thorough understanding of the mechanisms at the