  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 wildtype 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 GDNF-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.
