Axes, boundaries and coordinates: The ABCs of fly leg development

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Abstract
Recent studies of gene expression in the developing fruitfly leg support a model--Meinhardt's Boundary Model--which seems to contradict the prevailing paradigm for pattern formation in the imaginal discs of Drosophila--the Polar Coordinate Model. Reasoning from geometric first principles, this article examines the strengths and weaknesses of these hypotheses, plus some baffling phenomena that neither model can comfortably explain. The deeper question at issue is: how does the fly's genome encode the three-dimensional anatomy of the adult? Does it demarcate territories and boundaries (as in a geopolitical map) and then use those boundaries and their points of intersection as a scaffolding on which to erect the anatomy (the Boundary Model)? Or does it assign cellular fates within a relatively seamless coordinate system (the Polar Coordinate Model)? The existence of hybrid Cartesian-polar models shows that the alternatives may not be so clear-cut: a single organ might utilize different systems that are spatially superimposed or temporally sequential.