Figure 10.

Branching as a result of a diffusion-based geometry effect. (a) A cartoon of the proposed geometry-based branching mechanism. As a result of stronger diffusion-based loss at the edges, the concentration of the signal is highest in the centre of the domain (red line), and drives the outgrowth of a bud. As the bud elongates, more signal is lost at the tip than at the sides, because of the higher curvature, and a bifurcating concentration profile of the signalling factor emerges. Computational studies confirm that the geometry effect results in bifurcating concentration profiles, but reveals that it does not support bifurcating outgrowth (D. Menshykau & D. Iber 2013, unpublished data). (b) The simulated concentration profile of a ligand that is uniformly secreted from the epithelium of extracted three-dimensional chicken lung bud (Hamburger–Hamilton (HH) stage 27+) into a large computational bounding box [58]. The concentration profiles were normalized to the highest value (red, highest relative concentration; blue, lowest). (c) (i) A three-dimensional solid model representation of the region of highest ligand concentration represented by the red shading. (ii) The morphogen concentration in a cross-section through a bud. The bud stalk and branch point have a local maximum (solid white triangles), whereas the bud tip has a local minimum (empty black triangles) in the predicted ligand concentration [58].