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.

Many organs of higher organisms are heavily branched structures and arise by an apparently similar process of branching morphogenesis. Yet the regulatory components and local interactions that have been identified differ greatly in these organs. It is an open question whether the regulatory processes work according to a common principle and how far physical and geometrical constraints determine the branching process. Here, we review the known regulatory factors and physical constraints in lung, kidney, pancreas, prostate, mammary gland and salivary gland branching morphogenesis, and describe the models that have been formulated to analyse their impacts.

Early branching events during lung development are stereotyped. Although key regulatory components have been defined, the branching mechanism remains elusive. We have now used a developmental series of 3D geometric datasets of mouse embryonic lungs as well as time-lapse movies of cultured lungs to obtain physiological geometries and displacement fields. We find that only a ligand-receptor-based Turing model in combination with a particular geometry effect that arises from the distinct expression domains of ligands and receptors successfully predicts the embryonic areas of outgrowth and supports robust branch outgrowth. The geometry effect alone does not support bifurcating outgrowth, while the Turing mechanism alone is not robust to noisy initial conditions. The negative feedback between the individual Turing modules formed by fibroblast growth factor 10 (FGF10) and sonic hedgehog (SHH) enlarges the parameter space for which the embryonic growth field is reproduced. We therefore propose that a signaling mechanism based on FGF10 and SHH directs outgrowth of the lung bud via a ligand-receptor-based Turing mechanism and a geometry effect.