A non-linear vector field model of supernumerary limb production in salamanders

Abstract

We critically analyze current data on supernumerary production in grafting experiments with salamanders and formulate a vector field model which captures the essence of these results in a unified and quantitative manner. The motivation for this work has been the difficulty other models have had in accounting for the data concerning ipsilateral grafts. The source of this difficulty is rooted in the boundary conditions imposed by continuity at the interfaces between the intercalary region and the stump and blastema tissues. In our approach supernumeraries arise in the intercalary region of the grafts as a result of symmetry-breaking bifurcations in the pattern specification field. This requires the pattern field to obey a non-linear dynamics which effects a coupling between the axial and proximo-distal components of the field. Steady state solutions of the model are presented which correspond to the production of normal supernumeraries. The number, positions and handedness of supernumeraries is, in general, well-predicted by the model for both contralateral and ipsilateral grafts. Twelve specific predictions are made which suggest future possible experiments.