Kidney branching morphogenesis under the control of a ligand–receptor-based Turing mechanism

The main signalling proteins that control early kidney branching have been defined. Yet the underlying mechanism is still elusive. We have previously shown that a Schnakenberg-type Turing mechanism can recapitulate the branching and protein expression patterns in wild-type and mutant lungs, but it is unclear whether this mechanism would extend to other branched organs that are regulated by other proteins. Here, we show that the glial cell line-derived neurotrophic factor–RET regulatory interaction gives rise to a Schnakenberg-type Turing model that reproduces the observed budding of the ureteric bud from the Wolffian duct, its invasion into the mesenchyme and the observed branching pattern. The model also recapitulates all relevant protein expression patterns in wild-type and mutant mice. The lung and kidney models are both based on a particular receptor–ligand interaction and require (1) cooperative binding of ligand and receptor, (2) a lower diffusion coefficient for the receptor than for the ligand and (3) an increase in the receptor concentration in response to receptor–ligand binding (by enhanced transcription, more recycling or similar). These conditions are met also by other receptor–ligand systems. We propose that ligand–receptor-based Turing patterns represent a general mechanism to control branching morphogenesis and other developmental processes. (paper)