  In vitro cultures of endothelial cells are a widely used model system of the
collective behavior of endothelial cells during vasculogenesis and
angiogenesis. When seeded in an extracellular matrix, endothelial cells can
form blood vessel-like structures, including vascular networks and sprouts.
Endothelial morphogenesis depends on a large number of chemical and mechanical
factors, including the compliancy of the extracellular matrix, the available
growth factors, the adhesion of cells to the extracellular matrix, cell-cell
signaling, etc. Although various computational models have been proposed to
explain the role of each of these biochemical and biomechanical effects, the
understanding of the mechanisms underlying in vitro angiogenesis is still
incomplete. Most explanations focus on predicting the whole vascular network or
sprout from the underlying cell behavior, and do not check if the same model
also correctly captures the intermediate scale: the pairwise cell-cell
interactions or single cell responses to ECM mechanics. Here we show, using a
hybrid cellular Potts and finite element computational model, that a single set
of biologically plausible rules describing (a) the contractile forces that
endothelial cells exert on the ECM, (b) the resulting strains in the
extracellular matrix, and (c) the cellular response to the strains, suffices
for reproducing the behavior of individual endothelial cells and the
interactions of endothelial cell pairs in compliant matrices. With the same set
of rules, the model also reproduces network formation from scattered cells, and
sprouting from endothelial spheroids. Combining the present mechanical model
with aspects of previously proposed mechanical and chemical models may lead to
a more complete understanding of in vitro angiogenesis.
