  We explain the principles of gene expression pattern stabilization in systems
of interacting, diffusible morphogens, with dynamically established source
regions. Using a reaction-diffusion model with step-function production term,
we identify the phase transition between low-precision indeterminate patterning
and the phase in which a traveling, well-defined contact zone between two
domains is formed. Our model analytically explains single- and two-gene domain
dynamics and provides pattern stability conditions for all possible two-gene
regulatory network motifs.
