Figure 9.

Patterning models based on the local variations in the distance of the epithelium from the source of FGF10. (a) Branching as a result of diffusion-limited growth. Tissue (delimited by white line) that is placed into a solution with a low concentration of an outgrowth-inducing signalling factor (such as FGF10 in the lung) will degrade the signalling factor and thus induce a concentration gradient (red, high; blue, low). As a result of small irregularities in the tissue shape (white line), some part of the tissue will be closer to the higher concentration and accordingly start to grow out faster, thus experiencing even higher (relative) concentrations; adapted from Hartmann & Miura [48]. (b) With FGF10 produced mainly in the submesothelial mesenchyme and its receptor produced only in the epithelium, an FGF10 gradient can be expected to emerge. If the FGF10 concentration is homogeneous close to the mesothelium and on the epithelium, then the gradient would be steeper, the shorter the distance between epithelium and mesothelium. If cells read out gradients rather than concentration, then small differences in the distance could trigger self-avoiding outgrowth of branches; adapted from Clément et al. [49]. (c–e) Distance-based mechanism based on SHH and FGF10. SHH is produced only by the epithelium, and represses Fgf10 expression at high concentrations. Accordingly, Fgf10 expression can be expected to be lower, the closer are epithelium and mesothelium [12]. (c) Assuming that SHH induces Fgf10 expression at low concentrations, the FGF10 concentration is high as long as the bud is sufficiently far away from the boundary, thus supporting bud elongation. (d) As the bud approaches the impermeable boundary, the FGF10 profile splits, thus supporting bifurcating outgrowth. (e) The bifurcation in (d) requires an impermeable boundary and is not observed on an open domain. The FGF10 distribution in (c–e) was calculated according to the model presented by Hirashima & Iwasa [11]. (c–e) Adapted from Menshykau et al. [50].