Burgers Dynamics and Self-Assembly of Endothelial Cell Networks

Supply of nutrients to tissues is carried out by capillaries. Capillary patterns are mimicked by endothelial cells cultured on basement membrane proteins. On this surface, single randomly dispersed cells organize to form a two dimensional network and later fold up creating a net of capillary-like chords. By varying the average surface density of deposed cells a percolative transition is observed: for low enough disconnected structures are formed instead of a single connected network. We present a model for this morphogenetic process based on a multi dimensional version of Burgers equation. Supported by numerical and experimental evidence, we propose a mechanism linking the scale of formed endothelial structures to the range of cell-cell interaction mediated by the release of soluble molecules