A hierarchical polar coordinate model for epimorphic regeneration.

In the framework of polar coordinates three rules are postulated which can describe epimorphic regeneration in amphibian limbs. The rules can be seen as an extension of the polar coordinate model. When cells with different positional values are confronted, cell proliferation at the junction restores the continuity of positional values. Reestablishment of continuity is associated with the eventual congruence of the intercalating cell sequence with the host or graft, or both. The intercalating contours can be simple or twisted. The possible contours are graded within a plausible hierarchical scheme where congruent paths are favored versus non-congruent paths and simple contours are favored versus twisted contours. The model correctly predicts the multiplicity, position and different structures of supernumerary outgrowths resulting from both contralateral graftings and 180 degrees ipsilateral limb rotations. Development and regeneration of mirror-symmetric limbs are also accounted for. Several other experimental results are in agreement with the model. Many model predictions and correlations still remain to be tested.