  Kidney branching morphogenesis has been studied extensively, but the
mechanism that defines the branch points is still elusive. Here we obtained a
2D movie of kidney branching morphogenesis in culture to test different models
of branching morphogenesis with physiological growth dynamics. We carried out
image segmentation and calculated the displacement fields between the frames.
The models were subsequently solved on the 2D domain, that was extracted from
the movie. We find that Turing patterns are sensitive to the initial conditions
when solved on the epithelial shapes. A previously proposed diffusion-dependent
geometry effect allowed us to reproduce the growth fields reasonably well, both
for an inhibitor of branching that was produced in the epithelium, and for an
inducer of branching that was produced in the mesenchyme. The latter could be
represented by Glial-derived neurotrophic factor (GDNF), which is expressed in
the mesenchyme and induces outgrowth of ureteric branches. Considering that the
Turing model represents the interaction between the GDNF and its receptor RET
very well and that the model reproduces the relevant expression patterns in
developing wildtype and mutant kidneys, it is well possible that a combination
of the Turing mechanism and the geometry effect control branching
morphogenesis.
