Blood vessels form either when dispersed endothelial cells (the cells lining the inner walls of fully formed blood vessels) organize into a vessel network (vasculogenesis), or by sprouting or splitting of existing blood vessels (angiogenesis). Although they are closely related biologically, no current model explains both phenomena with a single biophysical mechanism. Most computational models describe sprouting at the level of the blood vessel, ignoring how cell behavior drives branch splitting during sprouting. We present a cell-based, Glazier–Graner–Hogeweg model (also called Cellular Potts Model) simulation of the initial patterning before the vascular cords form lumens, based on plausible behaviors of endothelial cells. The endothelial cells secrete a chemoattractant, which attracts other endothelial cells. As in the classic Keller–Segel model, chemotaxis by itself causes cells to aggregate into isolated clusters. However, including experimentally observed VE-cadherin–mediated contact inhibition of chemotaxis in the simulation causes randomly distributed cells to organize into networks and cell aggregates to sprout, reproducing aspects of both de novo and sprouting blood-vessel growth. We discuss two branching instabilities responsible for our results. Cells at the surfaces of cell clusters attempting to migrate to the centers of the clusters produce a buckling instability. In a model variant that eliminates the surface–normal force, a dissipative mechanism drives sprouting, with the secreted chemical acting both as a chemoattractant and as an inhibitor of pseudopod extension. Both mechanisms would also apply if force transmission through the extracellular matrix rather than chemical signaling mediated cell–cell interactions. The branching instabilities responsible for our results, which result from contact inhibition of chemotaxis, are both generic developmental mechanisms and interesting examples of unusual patterning instabilities.

Vascular and nonvascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm-blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear segments. To explain the emergence of such structures, we propose a simple model of preferential attraction to stretched cells. Numerical simulations reveal that the model evolves into a quasistationary pattern containing linear segments, which interconnect above the critical volume fraction of 0.2. In the quasistationary state, the generation of new branches offset the coarsening driven by surface tension. In agreement with empirical data, the characteristic size of the resulting polygonal pattern is density-independent within a wide range of volume fractions.

Embryonic and fetal vascular sprouts form within constantly expanding tissues. Nevertheless, most biological assays of vascular spouting are conducted in a static mechanical milieu. Here we study embryonic mouse allantoides, which normally give raise to an umbilical artery and vein. However, when placed in culture, allantoides assemble a primary vascular network. Unlike other in vitro assays, allantoic primordial vascular cells are situated on the upper surface of a cellular layer that is engaged in robust spreading motion. Time-lapse imaging allows quantification of primordial vascular cell motility as well as the underlying mesothelial tissue motion. Specifically, we calculate endothelial cell-autonomous motion by subtracting the tissue-level mesothelial motion from the total endothelial cell displacements. Formation of new vascular polygons is hindered by administration of function-blocking VE-cadherin antibodies. Time-lapse recordings reveal that (1) cells at the base of sprouts normally move distally "over" existing sprout cells to form new tip-cells; and (2) loss of VE-cadherin activity prevents this motile behavior. Thus, endothelial cell-cell-adhesion-based motility is required for the advancement of vascular sprouts within a moving tissue environment. To the best of our knowledge, this is the first study that couples endogenous tissue dynamics to assembly of vascular networks in a mammalian system.

Primary vascular plexus patterning, before the onset of circulation, is a collective action of primordial endothelial cells. To understand the patterning mechanism, we combined time‐lapse imaging of avian embryos and mouse allantoic explants with computer modeling. Endothelial cells were visualized through fluorescence‐labeled antibodies in time‐lapse recordings lasting up to 24hrs. Integrin, VEGF and VE cadherin function was perturbed by monoclonal antibodies. Cell‐autonomous motility and tissue motion was calculated from the image sequences. Our data revealed that primary vascular plexus formation involves the elongation of vasculogenic sprouts. Utilizing avb3 integrins, these multicellular sprouts invade rapidly into avascular areas, eventually creating a polygonal pattern. Sprout elongation, in turn, depends on a continuous supply of endothelial cells, streaming along the sprout towards its tip. Blocking VE cadherin function can substantially reduce the endothelial cell streaming behavior. To demonstrate that cell‐cell contact interactions are sufficient to produce polygonal patterns, we formulated and analyzed a simple mathematical model. The model exhibits robust sprouting dynamics and results in patterns with morphometry similar native primordial vascular plexuses — without ancillary assumptions involving chemotaxis or chemomechanical signaling. The results show that vasculogenic sprouts are of central importance in controlling the geometry of the primordial vascular network, representing an important target for neovascularization strategies, and tissue engineering. Support: American Heart Association 0535245N, 0410084Z; NIH info:ddbj-emblgenbank/HL068855 and the Mathers Charitable Foundation.

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