  Many organs of higher organisms, such as the vascular system, lung, kidney,
pancreas, liver and glands, are heavily branched structures. The branching
process during lung development has been studied in great detail and is
remarkably stereotyped. The branched tree is generated by the sequential,
non-random use of three geometrically simple modes of branching (domain
branching, planar and orthogonal bifurcation). While many regulatory components
and local interactions have been defined an integrated understanding of the
regulatory network that controls the branching process is lacking. We have
developed a deterministic, spatio-temporal differential-equation based model of
the core signaling network that governs lung branching morphogenesis. The model
focuses on the two key signaling factors that have been identified in
experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well
as the SHH receptor patched (Ptc). We show that the reported biochemical
interactions give rise to a Schnakenberg-type Turing patterning mechanisms that
allows us to reproduce experimental observations in wildtype and mutant mice.
The kinetic parameters as well as the domain shape are based on experimental
data where available. The developed model is robust to small absolute and large
relative changes in the parameter values. At the same time there is a strong
regulatory potential in that the switching between branching modes can be
achieved by targeted changes in the parameter values. We note that the sequence
of different branching events may also be the result of different growth
speeds: fast growth triggers lateral branching while slow growth favours
bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is
sufficient to generate pattern that correspond to the observed branching modes
