Pattern Regulation in Epimorphic Fields: Cells may make use of a polar coordinate system for assessing their positions in developing organs.

Abstract

We have described a formal model for pattern regulation in epimorphic fields in which positional information is specified in terms of polar coordinates in two dimensions. We propose that cells within epimorphic fields behave according to two simple rules, the shortest intercalation rule and the complete circle rule, for both of which there is direct experimental evidence. It is possible to understand a large number of different behaviors of epimorphic fields as a straight-forward consequence of these two rules, and the model therefore provides a context in which to view many of the results of experimental embryology. Although we have confined our discussion to cockroach legs, the imaginal disks of Drosophila, and regenerating and developing amphibian limbs, the fact that the model can explain regulative behavior in such evolutionarily diverse animals suggests that it may have general applicability to epimorphic fields. The predictions which the model makes should make it possible to assess its applicability to other developing systems, and to investigate the cellular mechanisms involved.